Problem Solving

If a rectangle With Width 49.872 inches and length 30.64 inches has an area that is 15 times the area of a certain square, which of the following is the closest approximation to the length, in inches, of a side of that square?

(A)5
(B)10
(C)15
(D)20
(E)25

The OA is B.

Should I multiply the numbers or can I work with approximations?

Hello M7MBA.

The area of a rectangle is $$A_R=W\cdot L.$$

Let's take the aproximations $$W\approx50\ and\ L\approx30.$$ So, we will get $$A_R\approx50\cdot30\approx1500.$$

Now, the area of a square is $$A_S=a^2$$ where a is the length of each side. Now, we can set the equation $$A_R=15\cdot A_S\ <=>\ 1500\approx15\cdot a^2$$ $$a^2\approx100\ <=>a\approx10.$$

So, the answer is option B.

I hope this can help you.

I'm available if you'd like any follow up.