A rectangular garden has a perimeter of 48 cm and an area of 140 sq. cm. What is the width of this garden? A.) 12 cm B.) 10 cm C

Question

3 years ago

12

.) 10 in. D.) 12 sq. cm.

1 answer:

irakobra [83] · Answer 1 · 2022-05-10T21:03:59+03:00

Perimeter: 2W +2L = 48

Area = L x W = 140

Rewrite the area to solve for L: L = 140/W

Now replace that in the perimeter formula:

2W + 2(140/W) = 48

Divide all terms by 2:

W + 140/W = 24

Divide both sides by W:

140 + w^2 = 24w

Subtract 24w from both sides:

w^2 - 24w + 140 = 0

Factor:

(w-10) (w-14) = 0

Solve for each w for 0:

10-10 - 10 and 14-14 = 0

So the 2 dimensions are 10 and 14 cm.

14 isn't a choice so the answer is B. 10 cm.