Question

The length of one of the legs of a right angled triangle exceeds of the other leg by 10 cm but is smaller than that of the hypotenuse by 10 cm. Then the length of hypotenuse is:

• A. 50 cm
• B. 80 cm
• C. 70 cm
• D. none

Answer 1

The correct option is A 50 cm

In $\Delta ABC,\angle B=90°\Rightarrow Ac=hypotenuse$

$AB\&BC$ are two legs.

Let $AB>AC$

Given one leg exceeds the other by $10cm$

$\therefore AB=10+BC$

Let $AB$ be $xcm$

$\therefore BC=(x-10)cm,AC=(10+x)cmA{B}^2+B{C}^2=A{C}^2$ (Pythagoras theorem)

$\therefore x^2+(x-10{)}^2=(10+x{)}^2\therefore x^2+x^2+{10}^2-20x={10}^2+x^2+20x$

$\therefore$ length of hypotenuse$=AC=(x+10)=50cm$