The perimeter of a rectangular garage is 42 meters. The area is 98 square meters. What are the dimensions of the garage?

Answer 1

P = 42

A = 98 = LW, so L = 98/W

P = 42 = 2L + 2W

42 = 2(98/W) + 2W

42 = 196/W + 2W Mult by W to eliminate fraction

42W = 196 + 2W² Put into quadratic form

2W² - 42W + 196 = 0 Divide by 2

W² - 21W + 98 = 0 Factor

(W - 14)(W - 7) = 0

W = 14 or W = 7 and L = 7 or 14.

Answer 2

A=98 = Lw

P/2 = 42/2 =21 = L+w

L= 21-w

(21-w)w = 98

21w-w^2 = 98

w^2 -21w +98=0

(w-7)(w-14) = 0

w=7 or 14

L = 14 or 7

dimensions are 7 by 14 meters

Answer 3

L + W = 21, W = 21 - L

LW = 98

L(21 - L) = 98

21L - L² = 98

0 = L² - 21L + 98

0 = (L - 14)(L - 7)