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?

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Answer 1 · 2017-07-19T11:42:40

$x = 5 . c m$ $x=5color(white)(.)cm$

Area is width times length.

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

Area $\to w L = 35 c m^{2}$ $->wL=35 cm^2$

Drop the units of measurement for now

$x \times (x + 2) = 35$ $x xx (x+2) = 35$

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

Subtract 35 from both sides

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

Notice that $5 \times 7 = 35 and 7 - 5 = 2$ $5xx7=35 and 7-5=2$

Factorising

$(x - 5) (x + 7) = 0 \Rightarrow x = 5 and - 7$ $(x-5)(x+7)=0" " =>" " x=5 and -7$

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

$x = 5 . c m$ $x=5color(white)(.)cm$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check
$w = x = 5$ $w=x=5$
$L = x + 2 = 7$ $L=x+2=7$

Area $= 5 \times 7 = 35$ $=5xx7=35$ as expected