Question

The sides of a triangle are 5, 12 and 13 units. A rectangle of width 10 units is constructed equal in area to the area of the triangle. Then, the perimeter of the rectangle is 

(a) 30 units 

(b) 26 units 

(c) 13 units 

(d) 15 units

Answer 1

(b) 26 units

By Pythagoras theorem, we find that the given triangle is a right angled triangle with 12 as height and 5 as base.

∴ Area of the triangle = \(\frac12\) x 12 x 5 sq. units = 30 sq. units

∴ Area of the rectangle = length × breadth = 30

⇒ Length = \(\frac{30}{breadth}=\frac{30}{10}\)= 3 units 

∴ Perimeter of the rectangle = 2 × (10 + 3) units = 26 units.