Page 41 - Math Course 2 (Book 1)

Algebraic Equations: Use Formulas

Find Areas and Lengths of
Method 2 Solve for r f rst.
Rectangles

d = rt Write the formula.
d rt Examples
= Divide each side by t.
t t
d Find the area of a rectangle with length 14 feet and
= r Simplify.
t width 6 feet.
135
= r Replace d with 135 and t
3 A = ℓw Write the formula.
with 3.
45 = r Simplify. A = 4 • 6 Replace ℓ with 14 and w with 6.

The average speed is 45 miles A = 84 Simplify.
Answer
per hour.
Answer The area is 84 square feet.
Find Perimeters and Lengths of

Rectangles The area of a rectangle is 40 square meters. Its
length is 8 meters. Find its width.
Examples 15 cm Method 1 Substitute, then solve for the variables.

A = ℓw Write the formula.
20 cm
Find the perimeter of the rectangle. 40 = 8w Replace A with 40 and ℓ with 8.
P = 2(ℓ + w) Write the formula. 5 = w Mentally divide each side by 8.

P = 2(20 + 15) Replace ℓ with 20 and w Method 2 Solve, then substitute.
with 15.
A = ℓw Write the formula.
P = 2(35) Add 20 and 15.
A ℓw
= Divide each side by ℓ.
P = 70 Simplify. ℓ ℓ
A
= w Simplify.
ℓ
Answer The perimeter is 70 centimeters. 40
= w Replace A with 40 and ℓ with 8.
8
5 = w Simplify.
The perimeter of a rectangle is 60 feet. Its width is 9
feet. Find its length.
Answer The width is 5 meters.
P = 2ℓ + 2w Write the formula.

60 = 2ℓ + 2(9) Replace P with 60 and w
with 9.

60 = 2ℓ + 18 Simplify.

60 – 18 = 2ℓ + 18 –18 Subtract 18 from each side.

42 = 2ℓ Simplify.

21 = ℓ Mentally divide each side by 2.

Answer The length is 21 feet.

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