3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem

Angle sums and triangle properties, right-triangle side lengths from the Pythagorean relation, and perimeter and area of rectangles.

Elementary Algebra 2e, 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem

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53 exercises

3.4 Exercise 1

Before you get started, take this readiness quiz.

Simplify: $\frac{1}{2} \left(6 h\right) .$
If you missed this problem, review the reference.

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3.4 Exercise 2

The length of a rectangle is three less than the width. Let w represent the width. Write an expression for the length of the rectangle.
If you missed this problem, review the reference.

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3.4 Exercise 3

Solve: $A = \frac{1}{2} b h$ for b when $A = 260$ and $h = 52 .$
If you missed this problem, review the reference.

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3.4 Exercise 4

Simplify: $\sqrt{144} .$
If you missed this problem, review the reference.

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3.4 Exercise 6

The measures of two angles of a triangle are 31 and 128 degrees. Find the measure of the third angle.

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3.4 Exercise 7

The measures of two angles of a triangle are 49 and 75 degrees. Find the measure of the third angle.

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3.4 Exercise 9

The perimeter of a triangular garden is 48 feet. The lengths of two sides are 18 feet and 22 feet. How long is the third side?

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3.4 Exercise 10

The lengths of two sides of a triangular window are seven feet and five feet. The perimeter is 18 feet. How long is the third side?

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3.4 Exercise 12

The area of a triangular painting is 126 square inches. The base is 18 inches. What is the height?

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3.4 Exercise 13

A triangular tent door has an area of 15 square feet. The height is five feet. What is the base?

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3.4 Exercise 15

One angle of a right triangle measures $56 ° .$ What is the measure of the other small angle?

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3.4 Exercise 16

One angle of a right triangle measures $45 ° .$ What is the measure of the other small angle?

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3.4 Exercise 18

The measure of one angle of a right triangle is 50° more than the measure of the smallest angle. Find the measures of all three angles.

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3.4 Exercise 19

The measure of one angle of a right triangle is 30° more than the measure of the smallest angle. Find the measures of all three angles.

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3.4 Exercise 30

The length of a rectangle is 120 yards and the width is 50 yards. What is the perimeter?

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3.4 Exercise 31

The length of a rectangle is 62 feet and the width is 48 feet. What is the perimeter?

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3.4 Exercise 33

The area of a rectangle is 598 square feet. The length is 23 feet. What is the width?

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3.4 Exercise 34

The width of a rectangle is 21 meters. The area is 609 square meters. What is the length?

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3.4 Exercise 36

Find the length of a rectangle with: perimeter 80 and width 25.

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3.4 Exercise 37

Find the length of a rectangle with: perimeter 30 and width 6.

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3.4 Exercise 39

The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.

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3.4 Exercise 40

The length of a rectangle is eight feet more than the width. The perimeter is 60 feet. Find the length and width.

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3.4 Exercise 42

The length of a rectangle is eight more than twice the width. The perimeter is 64. Find the length and width.

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3.4 Exercise 43

The width of a rectangle is six less than twice the length. The perimeter is 18. Find the length and width.

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3.4 Exercise 45

The perimeter of a rectangular swimming pool is 200 feet. The length is 40 feet more than the width. Find the length and width.

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3.4 Exercise 46

The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width.

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3.4 Exercise 47

Solve using triangle properties.

The measures of two angles of a triangle are 26 and 98 degrees. Find the measure of the third angle.

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3.4 Exercise 49

Solve using triangle properties.

The measures of two angles of a triangle are 105 and 31 degrees. Find the measure of the third angle.

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3.4 Exercise 51

Solve using triangle properties.

The perimeter of a triangular pool is 36 yards. The lengths of two sides are 10 yards and 15 yards. How long is the third side?

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3.4 Exercise 53

Solve using triangle properties.

If a triangle has sides 6 feet and 9 feet and the perimeter is 23 feet, how long is the third side?

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3.4 Exercise 55

Solve using triangle properties.

A triangular flag has base one foot and height 1.5 foot. What is its area?

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3.4 Exercise 57

Solve using triangle properties.

What is the base of a triangle with area 207 square inches and height 18 inches?

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3.4 Exercise 59

Solve using triangle properties.

One angle of a right triangle measures 33 degrees. What is the measure of the other small angle?

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3.4 Exercise 61

Solve using triangle properties.

One angle of a right triangle measures 22.5 degrees. What is the measure of the other small angle?

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3.4 Exercise 63

Solve using triangle properties.

The perimeter of a triangle is 39 feet. One side of the triangle is one foot longer than the second side. The third side is two feet longer than the second side. Find the length of each side.

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3.4 Exercise 65

Solve using triangle properties.

One side of a triangle is twice the shortest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.

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3.4 Exercise 67

Solve using triangle properties.

The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.

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3.4 Exercise 69

Solve using triangle properties.

The angles in a triangle are such that one angle is twice the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.

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