1. ## Geometry question

A rectangle is 4 inches wide by 7 inches long. When the length and width are increased by the same amount, the area is increased by 26 square inches. What are the dimensions of the new rectangle?

2. Originally Posted by almarie15j
A rectangle is 4 inches wide by 7 inches long. When the length and width are increased by the same amount, the area is increased by 26 square inches. What are the dimensions of the new rectangle?
Hint: Let the amount by which the length and width is increased be x. then the new width is 4 + x and the new length is 7 + x. find the area of this rectangle. now you must set up an equation. the area of this rectangle is 26 square inches more than the area of the original rectangle, so what equation do you think you must set up?

3. Originally Posted by almarie15j
A rectangle is 4 inches wide by 7 inches long. When the length and width are increased by the same amount, the area is increased by 26 square inches. What are the dimensions of the new rectangle?
$\displaystyle A_{\mbox{new}} - A_{\mbox{old}} = 26$

But $\displaystyle A_{\mbox{old}} = lw = 4\cdot 7 = 28$

And $\displaystyle A_{\mbox{new}} = (l+x)(w+l) = (4+x)(7+x)$

Thus,

$\displaystyle (x+4)(x+7) - 28 = 26$

Solve this equation thyself.