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)= (-bб √(D) )/(2a) \\ w_1= (2- √(324) )/(2*5)= (2-18)/(10)=-1.6 \ \ \O \\ w_2= (2+18)/(10)=2 cm`

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