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EXAMPLE 2

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

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EXAMPLE 2

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

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

  3. Solve the formula P = 2l + 2wfor 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 – 2w = l 2 for Example 2 GUIDED PRACTICE P = 2l + 2w Write perimeter formula. P – 2w = 2l Subtract 2w from each side. Divide each side by 2

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

  5. Solve the formula A = lwfor 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 w = l for Example 2 GUIDED PRACTICE A = lw Write perimeter formula. Divide each side by l

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

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

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

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

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

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

  12. Solve the formula for the variable in red. Then use the given information to find the value of the variable. (b1 + b2)h 7. Find hif b1 = 6in., A = b2 = 8in., and A = 70in.2 2(70) h= (6 + 8) 2A h= (b1 + b2) 1 2 for Example 2 GUIDED PRACTICE Write formula. Substitute 70for Aand 6 for b1and8for b2. h = 10 Simplify h = 10 in.

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