1. Rewrite a formula with three variables
EXAMPLE 2
Rewrite a formula with three variables
Solve the formula P = 2l + w for w. Then find the width of a rectangle with a length of 12 meters and a perimeter of 41 meters.
SOLUTION
Solve the formula for w.
STEP 1
P = 2l + 2w
Write perimeter formula.
P – 2l = 2w
Subtract 2l from each side.
P – 2l 2
= w
Divide each side by 2.

2. Rewrite a formula with three variables
EXAMPLE 2
Rewrite a formula with three variables
Substitute the given values into the rewritten formula.
STEP 2
41 – 2(12) 2
w =
Substitute 41 for P and 12 for l.
w = 8.5
Simplify.
The width of the rectangle is 8.5 meters.
ANSWER

3. Solve the formula for p = 2l + 2w for l STEP 1
GUIDED PRACTICE
for Example 2
Solve the formula P = 2l + 2w for l. Then find the length of a rectangle with a width of 7 inches and a perimeter of 30 inches. 3.
Solve the formula for p = 2l + 2w for l
STEP 1
P = 2l + 2w
Write perimeter formula.
P – 2w = 2l
Subtract 2w from each side.
P – 2w 2
= l
Divide each side by 2

4. Substitute the given values in.
GUIDED PRACTICE
for Example 2
STEP 2
Substitute the given values in. l
Formula for
P – 2w 2 =
30 – 2 (7) 2 =
Multiply. 16 2 =
Subtract. 8 =
Divide.
Length of rectangle is 8 in.
ANSWER

5. GUIDED PRACTICE for Example 2
Solve the formula A = lw for w. Then find the width of a rectangle with a length of 16 meters and an area of 40 square meters. 4.
Solve the formula for w
STEP 1
A = lw
Write perimeter formula. A l = w
Divide each side by l

6. Substitute the given values into rewrite formula.
GUIDED PRACTICE
for Example 2
STEP 2
Substitute the given values into rewrite formula.
w = A l
Write perimeter formula. = w 40 16
Subtract 40 from A and 16 for l.
w = 2.5
Divide
Write of rectangle is 2.5 m

7. GUIDED PRACTICE for Example 2
Solve the formula for the variable in red. Then use the given information to find the value of the variable.
A = 1 2 bh 5.
Find h if b = 12 m
and A = 84 m2.
A = 1 2 bh
Write perimeter formula.
2A = bh
Multiply each side by 2. = h 2A b
Divide each side by b

8. Find the value of h if b = 12m and A = 84m2.
GUIDED PRACTICE
for Example 2
Find the value of h if b = 12m and A = 84m2. = h 2A b
Find h if b = 12 m
and A = 84 m2. = h 2A b
Write formula. = h
2(84) 12
Substitute 84 for A and 12 for b.
h = 14
Simplify
h = 14m

9. GUIDED PRACTICE for Example 2
Solve the formula for the variable in red. Then use the given information to find the value of the variable.
A = 1 2 bh 6.
and A = 9 cm2.
Find b if h = 3 cm
A = 1 2 bh
Write perimeter formula.
2A = bh
Multiply each side by 2. = b 2A h
Divide each side by h

10. GUIDED PRACTICE for Example 2
Solve the formula for the variable in red. Then use the given information to find the value of the variable.
A = 1 2 bh 6.
and A = 9 cm2.
Find b if h = 3 cm = b 2A h
Write formula. = b
2(9) 3
Substitute 9 for A and 3 for b.
b = 6
Simplify
b = 6cm

11. GUIDED PRACTICE for Example 2
Solve the formula for the variable in red. Then use the given information to find the value of the variable.
A = 1 2 7.
(b1 + b2)h
Find h if b1 = 6 in.,
b2 = 8 in., and A = 70 in.2
A = 1 2
(b1 + b2)h
Write perimeter formula.
2A = (b1 + b2)h
Multiply each side by 2.
h = 2A
(b1 + b2)
Divide by (b1 + b2)

12. GUIDED PRACTICE for Example 2
Solve the formula for the variable in red. Then use the given information to find the value of the variable.
A = 1 2 7.
(b1 + b2)h
Find h if b1 = 6 in.,
b2 = 8 in., and A = 70 in.2
h = 2A
(b1 + b2)
Write formula.
h =
2(70)
(6 + 8)
Substitute 70 for A and 6 for b1 and 8 for b2.
h = 10
Simplify
h = 10 in.