Question

The hypotenuse and the semi-perimeter of a right triangle are 20 cm and 25 cm respectively. The other two sides of the triangle are ____ and ____.

• A. 16 cm, 12 cm
• B. 20 cm, 12 cm
• C. 20 cm, 16 cm
• D. 24 cm, 18 cm
• E. None of these

Answer 1

The correct option is A 16 cm, 12 cm

We have, $a+b+20=2\times 24$
$\therefore a+b=28$

By Pythagoras Theorem, $a^2+b^2=400$
$\because (a+b{)}^2={28}^2\Rightarrow ab=\frac{{28}^2-(a^2+b^2)}{2}=\frac{{28}^2-400}{2}=192\therefore a-b=\sqrt{(a+b{)}^2-4ab}=\sqrt{784-4\times 192}=4$
Solving (1) and (2), we get
$a=16cm$ and $b=12cm$