d A rectangular carpet has an area of 60 sq.m Job Exams Maths

# Area Calculation MCQ 10 (A rectangular carpet has an area of 60 sq.m)

Area Calculation MCQ 10: A rectangular carpet has an area of 60 sq.m its diagonal and longer side together equal 5 times the shorter side. The length of the carpet is:_________?

But according to formula of area of rectangle ;

$Area Of Rectangle= Length(Longer side)\times Breadth (Shorter side)$

i-e

$60 = L\times S$

or

$S=\frac{60}{L}$

or

$L=\frac{60}{S} —-(2$

Now consider the right angled triangle ABC. Here Pythagoras theorem says;

$(AC)^2=(AB)^2+(BC)^2$

but

AC=D, AB=L and BC= S    so we can write;

$D^2=L^2+S^2$

$D=\sqrt(L^2+S^2)$

Put this value of D in eq 1, we get;

$L+\sqrt(L^2+S^2=5S$

$==> \sqrt(L^2+S^2)=5S-L$

Taking square on both sides, we get;

$L^2+S^2=(5S-L)^2$

$L^2+S^2=L^2+25S^2-10SL$

$==>24S^2-10SL=0$

Taking 2 S as common;

$==> 2S(12S-5L)=0$

$L=\frac{12S}{5} —(3$

Comparing eq 2 and 3

$\frac{12S}{5}=\frac{60}{S}$

or

$s^2=25$

or

$S=5$

Here we ignore -5 because length can not be negative.

Putting this value of S in  eq 2 we get;

$L=\frac{60}{5}=12$

So the length or longer side is 12 meters

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