The area of the of a rectangle is 336 square inches. If the perimeter is 76. What is the shorter sides length?

hello:

the perimeter is : p = 2 (w + l)

The area is : A = w * l w : width l : length w?

2 (w + l) = 76

w * l = 336

you have the system:

w + l = 38 ... (1)

w * l = 336 ... (2)

by (1) : l = 38 - w

subst in (2) : w (38 - w) = 336

38w - w² = 336

w² - 38w + 336 = 0

delta = b² - 4ac when : a = 1 and b = - 38 c = 336

delta = (-38) ² - 4 (1) (336) = 1444 - 1344 = 100 = 10²

w1 = (38-10) / 2 = 14 (the shorter sides length)

w2 = (38+10) / 2 = 24 (refused)