Math Question: A pool at a park takes up an area of 540 square yards the length is 1 2/3 times as long as the width what are the dimensions of the pool

Since area of rectangles is always expressed as length times width, (A=l*w) we can start out the problem by substituting in for what we know. Since we know the area is 540, the equation becomes 540 = l*w. Let's change that to l*w = 540 so that the variables are on the left hand side of the equation. It's prettier. Now, since the length is 1 2/3 times as long as the width, we can create a simple equation using that sentence. "is" means "equals" in mathematics, so the sentence literally says l = 1 2/3 *w. Let's change 1 2/3 to 5/3 because it's a multiplication problem. Now, since l = 5/3 * w, we can substitute into the equation l*w = 540. We get 5/3*w*w = 540. That simplifies to 5/3*w^2 = 540. Now we just need to isolate w. Start by multiplying both sides by 3/5 because 3/5 will cancel out 5/3. So, w^2 = 3/5 * 540. 3/5 * 540 = 324 so... w^2 = 324. If you now take the square root of both sides, you get... w = 18. Plug 18 in for w in the original equation and you get l * 18 = 540. Divide both sides by 18 and you get... l = 30. So, the dimensions of the pool are 30 yards by 18 yards.
Answered On 04/22/2020 22:44