The length of a rectangle exceeds its breadth by 4cm. If the length is increased by 3cm and the breadth is increased by 2 cm, the new area exceeds the original area by 79 sq cm. How do you find the dimensions of the given rectangle?

May 13, 2018

13 cm and 17cm

Explanation:

$x \mathmr{and} x + 4$ are the original dimensions.
$x + 2 \mathmr{and} x + 7$ are the new dimensions

$x \left(x + 4\right) + 79 = \left(x + 2\right) \left(x + 7\right)$

${x}^{2} + 4 x + 79 = {x}^{2} + 7 x + 2 x + 14$

${x}^{2} + 4 x + 79 = {x}^{2} + 9 x + 14$

$4 x + 79 = 9 x + 14$

$79 = 5 x + 14$

$65 = 5 x$

$x = 13$