The length of a rectangle is 6 in. more than its width. Its area is 40 sq. in. How do you find the width of the rectangle?

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The length of a rectangle is 6 in. more than its width. Its area is 40 sq. in. How do you find the width of the rectangle?

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Answer 1 · 2016-12-09T02:32:02

The width of the rectangle is $4$ $4$ inches.

Explanation:

We consider the width of the rectangle as $x$ $x$ which will make the length $(x + 6)$ $(x+6)$ . Since we know the area, and the formula of a rectangle's area to be length $\times$ $xx$ breadth, we can write:

$x \times (x + 6) = 40$ $x xx (x+6)=40$

Open the brackets and simplify.

$x^{2} + 6 x = 40$ $x^2+6x=40$

Subtract $40$ $40$ from both sides.

$x^{2} + 6 x - 40 = 0$ $x^2+6x-40=0$

Factorise.

$x^{2} + 10 x - 4 x - 40 = 0$ $x^2+10x-4x-40=0$

$x (x + 10) - 4 (x + 10) = 0$ $x(x+10)-4(x+10)=0$

$(x - 4) (x + 10) = 0$ $(x-4)(x+10)=0$

$x - 4 = 0$ $x-4=0$ and $x + 10 = 0$ $x+10=0$

$x = 4$ $x=4$ and $x = - 10$ $x=-10$

The only possibility in the above problem is that $x = 4$ $x=4$ .

That will make the width $4$ $4$ and the length $(x + 6)$ $(x+6)$ which is $10$ $10$ , and the area $(4 \times 10)$ $(4xx10)$ which is $40$ $40$ .

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The length of a rectangle is 6 in. more than its width. Its area is 40 sq. in. How do you find the width of the rectangle?

1 Answer

Explanation:

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