The length of a rectangle is 4 inches more than its width. If 2 inches are taken from the length and added to the width and the figure becomes a square with an area of 361 square inches. What are the dimensions of the original figure?

Question

Eli Assouline · Accepted Answer

I found a length of #25"in"# and width of #21"in"#.

I tried this:

Hazel Anglin · Answer

undefined The original rectangle's dimensions are width: 15 inches, length: 19 inches.

Kennedy Adams · Answer

undefined Let's denote the width of the original rectangle as $ w $ inches. According to the given information, the length of the rectangle would then be $ w + 4 $ inches.

When 2 inches are taken from the length and added to the width, the new length becomes $ w + 4 - 2 = w + 2 $ inches, and the new width becomes $ w + 2 $ inches.

Since the figure becomes a square after this adjustment, the new length and width are equal. Thus, we can write:

$$ w + 2 = w + 2 $$

We also know that the area of this square is 361 square inches. The area of a square is calculated by squaring its side length. So, we have:

$$ (w + 2)^2 = 361 $$

Now, solve this equation to find the value of $ w $. After finding the value of $ w $, you can find the length of the original rectangle, which is $ w + 4 $.