quadratic equations

Question

The length of a rectangle is 5 times the width. The area is 720 square centimeters. Find the length and width of the rectangle.

Answer 1

A rectangle area is found by multiplying length by width.

A=lw

A= 720 l=5x w=x. You are not given the width so you use a variable to represent it as an unknown number. However, you do know that whatever its dimension Is, the length is five times it.

substitute in the values you have for the variables of the area formula. 720=(5x)(x) then solve for x. This would really be 720=5x^{2 .} Do inverse operations to get x by itself.

x=12 (width)

5x= 60 (length)

Answer 2

L = 5w

A = l*W

= (5w)w

= 5w^2

720 = 5w^2

144 = w^2

w^2 - 144 = 0

(w + 12)(w-12) = 0

w = -12 or w=12

width is 12, length is 60