Question

If the hypotenuse of a right angled triangle is $41cm$ and the area of the triangle is $180sq.cm$, find the difference between the lengths of the legs of the triangle

• A. $22cm$
• B. $25cm$
• C. $27cm$
• D. $31cm$

Answer 1

The correct option is D $31cm$

Consider the above figure,

Given,

$AC=41cm$ and Area of $△ABC=180c{m}^2$

We know that, by Pythagoras theorem

$A{B}^2+B{C}^2=A{C}^2$

$A{B}^2+B{C}^2={41}^2$ ...... $\left(i\right)$

$AreaofABC=\frac{1}{2}\times BC\times AB$

$BC\times AB=180\times 2=360$ ...... $\left(ii\right)$

We have,

$(AB-BC{)}^2=A{B}^2+B{C}^2-2\times AB\times BC$

Substitute from $\left(i\right)$ and $\left(ii\right)$ here,

$(AB-BC{)}^2={41}^2-2\times 360=1681-720=961$

$(AB-BC)=31cm$