Question

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

• A. $250$ sq.cm
• B. $200$ sq.cm
• C. $300$ sq.cm
• D. $275$ sq.cm

Answer 1

The correct option is D $275$ sq.cm

In right $△PQR$, using Pythagoras theorem,

${PR}^2={PQ}^2+{QR}^2\Rightarrow PR=\sqrt{{10}^2+5^2}=\sqrt{125}=5\sqrt{5}㎝$

Required area$=\frac{1}{2}\times 5\times 10+{\left(5\right)}^2+{\left(10\right)}^2+{\left(5\sqrt{5}\right)}^2$

$=25+25+100+125=275㎠$