Question

A rectangle is 4 cm longer than it is wide, and its area is 117 cm2 . find its dimensions.

Answer 1

the area of a rectangle is equal  L x  W   

4 cm longer than it is wide   L = 4 + W

L x  W = 117     we replace L here 

(4 + W ) x W = 117 

4W + W ^2  = 117 

4W + W ^2  -117 = 0
W ^2 +4 W -117 = 0

W² + 4W - 117 = 0


THEN u want to use the use the quadratic formula
 

OR Factoring gives us

(W + 13)(W - 9) = 0

W = -13 or 9

But it can't be negative, so

W = 9  and L= 9+4 = 13

Answer 2

The length and width of the rectangle are $13$ cm and $9$ cm respectively whose area is $117 cm^2$.

Let the width of the rectangle be $x$.

Then the length of the rectangle is $x+4$.

Area of a rectangle $=$ length $\times$ width

Area $= 117 cm^2$

$(x+4) \times x = 117$

$x^2+4x=117$

$x^2+4x-117=0$

$x^2+13x-9x-117=0$

$x(x+13)-9(x+13)=0$

$(x+13)(x-9)=0$

$x+13=0, x-9=0$

$x=-13, x=9$

Since, length cannot be negative. So, $x=-13$ is not possible.

So, $x=9$.

And $x+4=13$

So, length $= 13$ cm and width $= 9$ cm.

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