Question

the length of a rectangle is 27 centimeters less than five times its width. its area is 56 square centimeters. find the dimensions of the rectangle

Answer 1

A=LW
L is -27+5w

L=5w-27
sub that for L
A=(5w-27)w
56=5w^2-27w
minus 56 both sides
0=5w^2-27w-56
factor
0=(w-7)(5w+8)
set to zero
w-7=0
w=7

5w+8=0
5w=-8
w=-8/5
false, legnth cannot be neative

w=7

a=lw
56=l7
divide both sides by 7
8=l

it is 8cm by 7cm
legnth=8cm
width=7cm