Practice Makes Perfect
Solve a Formula for a Specific Variable
In the following exercises, solve the given formula for the specified variable.
1. Solve the formula C=πd for d.
- Answer
-
d=Cπ
2. Solve the formula C=πd for π.
3. Solve the formula V=LWH for L.
- Answer
-
L=VWH
4. Solve the formula V=LWH for H.
5. Solve the formula A=12bh for b.
- Answer
-
b=2Ah
6. Solve the formula A=12bh for h.
7. Solve the formula
A=12d1d2 for d1.
- Answer
-
d1=2Ad2
8. Solve the formula
A=12d1d2 for d2.
9. Solve the formula
A=12h(b1+b2) for b1.
- Answer
-
b1=2Ah−b2
10. Solve the formula
A=12h(b1+b2) for b2.
11. Solve the formula
h=54t+12at2 for a.
- Answer
-
a=2h−108tt2
12. Solve the formula
h=48t+12at2 for a.
13. Solve 180=a+b+c for a.
- Answer
-
a=180−b−c
14. Solve 180=a+b+c for c.
15. Solve the formula
A=12pI+B for p.
- Answer
-
p=2A−2BI
16. Solve the formula
A=12pI+B for I.
17. Solve the formula
P=2L+2W for L.
- Answer
-
L=P−2W2
18. Solve the formula
P=2L+2W for W.
In the following exercises, solve for the formula for y.
19. Solve the formula
8x+y=15 for y.
- Answer
-
y=15−8x
20. Solve the formula
9x+y=13 for y.
21. Solve the formula
−4x+y=−6 for y.
- Answer
-
y=−6+4x
22. Solve the formula
−5x+y=−1 for y.
23. Solve the formula
x−y=−4 for y.
- Answer
-
y=4+x
24. Solve the formula
x−y=−3 for y.
25. Solve the formula
4x+3y=7 for y.
- Answer
-
y=7−4x3
26. Solve the formula
3x+2y=11 for y.
27. Solve the formula
2x+3y=12 for y.
- Answer
-
y=12−2x3
28. Solve the formula
5x+2y=10 for y.
29. Solve the formula
3x−2y=18 for y.
- Answer
-
y=18−3x−2
30. Solve the formula
4x−3y=12 for y.
Use Formulas to Solve Geometry Applications
In the following exercises, solve using a geometry formula.
31. A triangular flag has area 0.75 square feet and height 1.5 foot. What is its base?
- Answer
-
1 foot
32. A triangular window has area 24 square feet and height six feet. What is its base?
33. What is the base of a triangle with area 207 square inches and height 18 inches?
- Answer
-
23 inches
34. What is the height of a triangle with area 893 square inches and base 38 inches?
35. The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.
- Answer
-
45°,\; 45°,\; 90°
36. The measure of the smallest angle of a right triangle is 20° less than the measure of the next larger angle. Find the measures of all three angles.
37. 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.
- Answer
-
30°,\; 60°,\; 90°
38. The angles in a triangle are such that one angle is 20 more than the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.
In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.
39.

- Answer
-
15
40.

41.

- Answer
-
25
42.

In the following exercises, use the Pythagorean Theorem to find the length of the unknown leg. Round to the nearest tenth if necessary.
43.

- Answer
-
8
44.

45.

- Answer
-
12
46.

47.

- Answer
-
10.2
48.

49.

- Answer
-
9.8
50.

In the following exercises, solve using a geometry formula.
51. The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.
- Answer
-
18 meters, 11 meters
52. The length of a rectangle is eight feet more than the width. The perimeter is 60 feet. Find the length and width.
53. The width of the rectangle is 0.7 meters less than the length. The perimeter of a rectangle is 52.6 meters. Find the dimensions of the rectangle.
- Answer
-
13.5 m, 12.8 m
54. The length of the rectangle is 1.1 meters less than the width. The perimeter of a rectangle is 49.4 meters. Find the dimensions of the rectangle.
55. The perimeter of a rectangle of 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.
- Answer
-
25 ft, 50 ft
56. The length of the rectangle is three times the width. The perimeter of a rectangle is 72 feet. Find the length and width of the rectangle.
57. The length of the rectangle is three meters less than twice the width. The perimeter of a rectangle is 36 meters. Find the dimensions of the rectangle.
- Answer
-
7 m, 11 m
58. The length of a rectangle is five inches more than twice the width. The perimeter is 34 inches. Find the length and width.
59. 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.
- Answer
-
12 ft, 13 ft, 14 ft
60. The perimeter of a triangle is 35 feet. One side of the triangle is five feet longer than the second side. The third side is three feet longer than the second side. Find the length of each side.
61. One side of a triangle is twice the smallest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.
- Answer
-
3 ft, 6 ft, 8 ft
62. One side of a triangle is three times the smallest side. The third side is three feet more than the shortest side. The perimeter is 13 feet. Find the lengths of all three sides.
63. The perimeter of a rectangular field is 560 yards. The length is 40 yards more than the width. Find the length and width of the field.
- Answer
-
120 yd, 160 yd
64. The perimeter of a rectangular atrium is 160 feet. The length is 16 feet more than the width. Find the length and width of the atrium.
65. A rectangular parking lot has perimeter 250 feet. The length is five feet more than twice the width. Find the length and width of the parking lot.
- Answer
-
40 ft, 85 ft
66. A rectangular rug has perimeter 240 inches. The length is 12 inches more than twice the width. Find the length and width of the rug.
In the following exercises, solve. Approximate answers to the nearest tenth, if necessary.
67. A 13-foot string of lights will be attached to the top of a 12-foot pole for a holiday display as shown. How far from the base of the pole should the end of the string of lights be anchored?

- Answer
-
5 feet
68. Pam wants to put a banner across her garage door diagonally, as shown, to congratulate her son for his college graduation. The garage door is 12 feet high and 16 feet wide. How long should the banner be to fit the garage door?

69. Chi is planning to put a diagonal path of paving stones through her flower garden as shown. The flower garden is a square with side 10 feet. What will the length of the path be?

- Answer
-
14.1 feet
70. Brian borrowed a 20-foot extension ladder to use when he paints his house. If he sets the base of the ladder six feet from the house as shown, how far up will the top of the ladder reach?
