The area of the rectangle is 35cm squared if the bottom and top of the rectangle are x+2 and the left and right side equals x, what is the expression of rectangle in terms of x?

Jul 19, 2017

$x = 5 \textcolor{w h i t e}{.} c m$

Explanation:

Area is width times length.

Let width (shortest) be $w = x$
Let the length be $L = x + 2$

Area$\to w L = 35 c {m}^{2}$

Drop the units of measurement for now

$x \times \left(x + 2\right) = 35$

${x}^{2} + 2 x = 35$

Subtract 35 from both sides

${x}^{2} + 2 x - 35 = 0$

Notice that $5 \times 7 = 35 \mathmr{and} 7 - 5 = 2$

Factorising

$\left(x - 5\right) \left(x + 7\right) = 0 \text{ " =>" } x = 5 \mathmr{and} - 7$

The -7 is not a logical solution for this question so ignore it

$x = 5 \textcolor{w h i t e}{.} c m$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check
$w = x = 5$
$L = x + 2 = 7$

Area $= 5 \times 7 = 35$ as expected