Question

The length of a rectangle is three inches more than the width. the area of the rectangle is 460 inches. if the width is x, what is the length in terms of x?

Answer 1

l=3+w (l=length, w=width)

l=3+x if x is the width

Answer 2

The length and width of the given rectangle are 23 and 20 inches respectively.

Suppose the width of the given rectangle=x inch

So, the length of the given rectangle = x+3 inch

What is the area of a rectangle?

The area of a rectangle with length l and width b is lb.

So, the area of the given rectangle = x(x+3)

Given that area of the rectangle = 460 squared inches

So, x(x+3)=460

$x^{2} +3x=460$

$x^{2} +x-460=0$

$x^{2} +23x-20x-460=0$

$x(x+23)-20(x+23) =0$

$(x+23) (x-20)=0$

$x=-23$...Not possible

$x=20$

The width of the rectangle =20 inches

So, the length of the rectangle =20+3 = 23 inches

Therefore, the length and width of the given rectangle are 23 and 20 inches respectively.

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