Question

The length of a rectangle is twice its width. Given the length of the diagonal is $5\sqrt{5}$, find the area of the rectangle.

Answer 1

Answer: Area of rectangle is 50 square units.

Step-by-step explanation:

Since we have given that

Diagonal of the rectangle = 5√5

Let the width of rectangle be 'x'

Let the length of rectangle be '2x'

As we know the formula for diagonal of rectangle:

$5\sqrt{5}=\sqrt{l^2+w^2}\\\\(5\sqrt{5}})^2=(2x)^2+x^2\\\\125=4x^2+x62\\\\125=5x^2\\\\\dfrac{125}{5}=x^2\\\\25=x^2\\\\x=\sqrt{25}\\\\x=5\ units$

So, Length of rectangle be 2x=2×5=10 units

And the area of the rectangle is given by

$Area=Length\times width\\\\Area=10\times 5\\\\Area=50\ sq.\ unit$

Hence, area of rectangle is 50 square units.