Question

The area of a rectangle is $36x^4$ and one of its sides is $4x$. A square is constructed on the other side. What is the ratio of the area of the square to that of the rectangle?

Answer 1

We know that the area of rectangle with sides $a$ and $b$ is $A=a\times b$.

Here, it is given that one of the side is $a=4x^2$ and the area of rectangle is $36x^4$, therefore, the other side $b$ is:

$36x^4=4x^2\times b\Rightarrow b=\frac{36x^4}{4x^2}=9x^2$

Since a square is constructed on the other side, thus, that side will be $9x^2$.

We know that the area of square with side $a$ is $A=a^2$.

Here, it is given that the side of the square is $9x^2$, therefore,

$A=\left[\right(9x{)}^2{]}^2=81x^4$

Therefore, the area of the square is $81x^4$.

Also, the area of rectangle given is $36x^4$

The ratio of the areas of square and rectangle is:

$\frac{81x^4}{36x^4}=\frac{9}{4}$

Hence, the ratio of the area of the square to that of the rectangle is $9:4$.