Question

Squares are constructed on the outer side of a right-angled triangle on each of its three sides. If the lengths of the two sides containing the right angle are $5cm$ and $10cm$ respectively, then the total area of the regions bounded by the diagram is :

• A. $250c{m}^2$
• B. $200c{m}^2$
• C. $300c{m}^2$
• D. $275c{m}^2$

Answer 1

The correct option is D $275c{m}^2$

Given, $AB=5cm$, $AC=10cm$
From right angled $\Delta ABC$,
$B{C}^2=A{B}^2+A{C}^2$
$=5^2+{10}^2=125$
$\therefore BC=\sqrt{125}=5\sqrt{5}cm$
Hence, total area of bounded region $=$ Area of sq. $AD+$ Area of sq. $AE+$ Area of sq. $CF+$ Area of $\Delta ABC$
$=(5{)}^2+(10{)}^2+(5\sqrt{5}{)}^2+\frac{1}{2}\times 5\times 10$
$=25+100+125+25=275c{m}^2$