Question

The area of a rhombus is $2016$ sq cm and its side is $65cm$. The lengths of the diagonals (in cm) respectively are

• A. $125,35$
• B. $126,32$
• C. $132,26$
• D. $135,25$

Answer 1

Answer: (B)

$126,32$

Let $x$ and $y$ be the length of diagonals.

Area of rhombus = $2016m^2\Rightarrow \frac{1}{2}\times x\times y=2016$

$\Rightarrow xy=4032{cm}^2⟶\left(1\right)$

we know that the diagonals of rhombus bisect each other at ${90}^0$.

$\therefore {\left(\frac{x}{2}\right)}^2+{\left(\frac{y}{2}\right)}^2={65}^2\Rightarrow x^2+y^2=16900⟶\left(2\right)$

${(x+y)}^2=x^2+y^2+2xy=16900+2\times 4032=24964$

$\Rightarrow x+y=\sqrt{24964}=158\Rightarrow x+y=158⟶\left(3\right)$

Similarly $x-y=94$ $⟶\left(4\right)$

Solving (3) and (4), we get $x=126$ & $y=32$