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.

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√(5)=√(l^2+w^2)\\\\(5√(5)})^2=(2x)^2+x^2\\\\125=4x^2+x62\\\\125=5x^2\\\\(125)/(5)=x^2\\\\25=x^2\\\\x=√(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* width\\\\Area=10* 5\\\\Area=50\ sq.\ unit`

Hence, area of rectangle is 50 square units.