The length of a rectangle is 6 inches greater than the width. The area is 91 inches square root. Find the length and the width

Answer 1

Area of Rectangle = L x W

L = 6 + W

Assuming you meant 91in² or 91 inches squared,

91in² = (6 + W) x W

91in² = 6W + W²

0 = W² + 6W - 91in²

Using factoring of quadratic equations, you get

(W-7)(W+13) = 0

expanding the above:

W x W = W²

-7 x W = -7W

13 x W = 13W

-7 x 13 = -91

Combined:

W² - 7W + 13W - 91 = 0

W² + 6W - 91 = 0

Using (W-7)(W+13) = 0,

W = 7 or -13

But you can't have a negative length so W = 7

Using the equation L from above, L = 6 + 7

L = 13

So the Length = 13 in and Width = 7 in

You can also use the quadratic formula to solve for W.

0 = W² + 6W - 91in²

where x is W

a = 1

b = 6

c = -91

W = (-6 + sqrt(6²-4(1)(6)))/(2(1)) = (-6+20)/2 = 7

W = (-6 - sqrt(6²-4(1)(6)))/(2(1)) =(-6-20)/2 = -13