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 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

Answer: (D)

275 sq cm

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