Question

the length of a rectangle is 2 cm less than five times the width. the area of the rectangle is 16 cm^2. find the length and width of the rectangle.

Answer 1

length = L
width = w

L = (5w-2) cm

$w(5w-2)=16 \\ 5w^2-2w-16=0 \\ D=b^2-4ac=(-2)^2-4*5*(-16)=324 \\ w_{1,2}= \frac{-bб \sqrt{D} }{2a} \\ w_1= \frac{2- \sqrt{324} }{2*5}= \frac{2-18}{10}=-1.6 \ \ \O \\ w_2= \frac{2+18}{10}=2 cm$

width = 2 cm
length = 5w-2 = 5*2-2 = 8 cm