Question

the length fo a rectangle is four greater than the width,the are is sixty. find the length & with of the rectangle?

Answer 1

Since we're told that the length is four greater than the width,
x = Width, x+4 = Length
The area of a rectangle is L*W, so (x)(x+4) = \[x^{2} + 4x\]
You're given that the area is 60, so \[x^{2} + 4x = 60\]
Move all of your terms to one side to solve: \[x^{2} + 4x - 60 = 0\]
Find the roots of your quadratic equation: \[(x+10)(x-6) = 0\]
So you have roots x = -10 and x = 6
It's impossible to have a length or width that's negative, so reject x = -10
In the beginning, we set x = width; we just calculated x to be 6, so the width = 6
The length is four greater than the width, so the length is x + 4 = 6 + 4 = 10.