Question

The hypotenuse of a right angled triangle is $41$ cm and the area of the triangle is $180$ sq. cm, then the difference between the lengths of the legs of the triangles must be

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

Answer 1

The correct option is C $31$ cm

Area $=180c{m}^2$

$\frac{ab}{2}=180ab=2\times 180=360$

Applying Pythagoras theorem on right triangle shown above;

$a^2+b^2={41}^2$

$a^2+b^2=1681$

$a^2+b^2-2ab=1681-2ab$

$(a-b{)}^2=1681-2(360)=1681-720=961$

$a-b=\sqrt{961}=31$ cm

The difference between the lengths of the legs of the triangles must be $31$ cm.