A rectangle has an area of $150$ $150$ $c m^{2}$ $cm^2$ . It has a length that is $5$ $5$ $c m$ $cm$ longer than its width. What is the rectangle's length?

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Answer 1 · 2017-07-03T00:46:20

length $= 15 c m$ $=15cm$
width $= 10 c m$ $=10cm$

$l \cdot w = A$ $l*w=A$

let $w = x$ $w=x$

let $l = x + 5$ $l=x+5$

$A = (x + 5) \cdot x$ $A=(x+5)*x$

and distribute: $150 = x^{2} + 5 x$ $150=x^2+5x$

move everything to one side: $x^{2} + 5 x - 150 = 0$ $x^2+5x-150=0$

factor: $(x + 15) \cdot (x - 10) = 0$ $(x+15)*(x-10)=0$

$x + 15 = 0$ $x+15=0$ ; $x = - 15$ $x=-15$
or
$x - 10 = 0$ $x-10=0$ ; $x = 10$ $x=10$
$x \neq - 15$ $x!=-15$ so $x = 10$ $x=10$

length $= 15 c m$ $=15cm$
width $= 10 c m$ $=10cm$

A rectangle has an area of 150150 cm2cm^2. It has a length that is 55 cmcm longer than its width. What is the rectangle's length?