If the length of a rectangle is increased by 20% and the width is increased by 30%, then by what percent is the area of the rectangle increased?
area with old dimensions: lw
new length = 1.2l
new width = 1.3w
new area = (1.2l)(1.3)w
= (1.2)(1.3) lw = 1.56 lw
increase = 1.56lw - lw = .56 lw
looks like the area increased by 56%
old A = LW
new A = 1.2L * 1.3W = 1.56 LW or a 56% increase
To find by what percentage the area of the rectangle is increased, we need to compare the initial area with the final area.
Let's say the initial length of the rectangle is L and the initial width is W. The initial area (A1) can be calculated as A1 = L * W.
After increasing the length by 20%, the new length becomes 1.2L (L + 20% of L) and after increasing the width by 30%, the new width becomes 1.3W (W + 30% of W). The new area (A2) can be calculated as A2 = 1.2L * 1.3W.
To find the percentage increase, we can use the formula:
Percentage Increase = [(Final Value - Initial Value) / Initial Value] * 100
Substituting the values, the percentage increase in the area can be calculated as:
[(A2 - A1) / A1] * 100
= [(1.2L * 1.3W - L * W) / (L * W)] * 100
Simplifying further:
= [(1.56 - 1) * 100] * 100
= 56%
Therefore, the area of the rectangle is increased by 56%.