Question

The perimeter of a right-triangular lawn is equal to 30 yards. The length of one of its sides is 10 yards. Find its hypotenuse.

• A. 15 yd
• B. 20 yd
• C. 12.5 yd
• D. 7.5 yd

Answer 1

The correct option is C 12.5 yd

Let AC = $a$, and AB = $b$.
Side BC = 10 yd
Perimeter = Sum of the sides
$\Rightarrow 30=a+10+b$
$\Rightarrow a+b=20$
$\Rightarrow b=20-a$ (Equation 1)
In $\Delta ABC$,
$A{C}^2=B{C}^2+A{B}^2$ (by Pythagorean theorem)
$\Rightarrow a^2={10}^2+b^2$
Using Equation 1, we get
$\Rightarrow a^2={10}^2+(20-a{)}^2$
$\Rightarrow a^2=100+{20}^2+a^2-2\times 20\times a\left[\right(a-b{)}^2=a^2+b^2-2ab]$
$\Rightarrow 0=100+400-40a$
$\Rightarrow 40a=500$
$\Rightarrow a=12.5$
The length of the hypotenuse = 12.5 yd
Hence, the correct answer is option B.