Question

Given the area, find the dimension of a rectangle

The width of a rectangle is 30 feet less than twice its length. its area is 68 square feet. Find the dimensions of the rectangle.​

Answer 1

Length L = 17 ft.

Width W = 4 ft

Explanation:

Area of a rectangle = L * W

Area = 68 ft²

W = 2L - 30

Area = L * W

68 = L * (2L - 30)

68 = 2L² - 30L

2L² - 30L -68 = 0 ( solve L by using quadratic equation)

-(-30) ± √ -30² - 4 * 2 * (-68)

L = -------------------------------------------

2 * 2

L = 17 ; L= - 2 therefore use L = 17 ft.

solve for W:

W = 2L - 30

W = 2(17) - 30

W = 34 - 30

W = 4 ft

check:

Area = L * W

68 = 17 * 4

68 = 68 ----- OK

Answer 2

Length=17

Width=4

Explanation:

Length=x

Width=2x-30

x(2x-30)=68

2x²-30x=68

2x²-30x-68=0

2(x²-15x-34)=0

2(x+2)(x-17)=0

So x equals either 17 or -2. Since it can’t be -2, x=17

Length=x=17

Width=2x-30=2*17-30=34-30=4