the length and width of a rectangle are each increased by 20%. by what percent is the rectangles area increased?
A = lw
(1.2*l)(1.2*w) = 1.44*lw = 1.44A
So, the area has increased by 44%
To find the answer, we need to calculate the new area of the rectangle and compare it to the original area. Let's break it down step by step:
1. Let's assume the original length of the rectangle is L and the original width is W.
2. The original area of the rectangle is given by A = L * W.
3. The length is increased by 20%, which means the new length is (L + (0.2 * L)) = (1.2 * L).
4. The width is also increased by 20%, so the new width is (W + (0.2 * W)) = (1.2 * W).
5. The new area of the rectangle is (1.2 * L) * (1.2 * W) = 1.44 * A.
Now, to find the percentage increase in the area, we can use the formula:
Percentage increase = ((New area - Original area) / Original area) * 100
Let's calculate it:
Percentage increase = ((1.44 * A - A) / A) * 100
= (0.44 * A / A) * 100
= 44%
Therefore, the area of the rectangle is increased by 44%.