Question

The length of hypotenuse of a right-angled triangle is 5 cm and its area is 6 $c{m}^2$ The lengths of the remaining sides are

• A. 4 cm and 2 cm
• B. 3 cm and 2 cm
• C. 1 cm and 3 cm
• D. 3 cm and 4 cm

Answer 1

The correct option is D 3 cm and 4 cm

$\frac{1}{2}ab=6\Rightarrow ab=12$
$a^2+b^2=5^2$
$a+b=\sqrt{a^2+b^2+2ab}=\sqrt{5^2+2\times 12}=7cm$
$a-b=\sqrt{a^2+b^2-2ab}=\sqrt{5^2-2\times 12}=1cm$
$a=\frac{1}{2}(7+1)=4cm;Thus,b=3cm.$