Question

yael used to have a square garage with 292ft^2 of floor space.she recently built an addition to it. The garage is still a​ square, but now it has​ 50% more floor space. What was the length of one side of the garage​ originally? What is the length of one side of the garage​ now? What was the percent increase in the length of one​ side?

Answer 1

Answer: 19

If the floor space of the garage is increased by 50%, that means its area is increased by that amount

So we have 228 + .50(228) = 228 + 114 = 342 ft²

Since the original garage is square-shaped with an area of 228 ft², then we can find the length of each side. If we let x = the side length, then we have:

x² = 228

x = 15.1 ft

Assuming that the garage will remain square-shaped with sides of uniform dimensions, then we can label each side of the expanded garage as 15 + y. We need to solve for y. Again, we use the area formula. Remember that the expanded garage will have an area of 342 ft², we now have:

(y + 15)² = 342

y² + 30y + 225 = 342

y² + 30y - 117 = 0

This can be solved using the Quadratic Formula. Remember that dimensions must always be positive. Once you determine y, then you will know what the length will be of the expanded garage