Question

A plot of land is in the shape of a right angled isosceles triangle. The length of the hypotenuse is $50\sqrt{2}m$. The cost of fencing it at Rs. $3$ per mete will be

• A. less than Rs. $300$
• B. less than Rs. $400$
• C. more than Rs. $500$
• D. more than Rs. $600$

Answer 1

The correct option is C more than Rs. $500$

In an isosceles right angled triangle, the two sides on the right angle are equal.
Hence, hypotenuse of the isosceles right angled triangle of side $a=\sqrt{a^2+a^2}=a\sqrt{2}$
Given, $a\sqrt{2}=50\sqrt{2}$
$a=50$
Hence, length of the other two sides of the triangle is $50m$
Perimeter of the triangle $=50+50+50\sqrt{2}=100+50\sqrt{2}=100+50\times 1.414=100+70.7=170.7m$
Cost of fencing it at Rs. $3$ per $m=3\times 170.7=$ Rs. $512.1$
Hence, the cost of fencing is more than Rs. $500$