If the base of an isosceles triangle is decreased by 40% and its height is increased by 10%, then what is the percent change in the area of the triangle?
i think it is 5o%
The percent change is a reduction to 66% of the original area, or a 34% reduction.
To find the percent change in the area of the triangle, we can follow these steps:
Step 1: Let's assume the original base of the isosceles triangle is B and the original height is H.
Step 2: The original area of the triangle is given by A = (1/2) * B * H.
Step 3: The new base after decreasing it by 40% is B' = B - 0.4B = 0.6B.
Step 4: The new height after increasing it by 10% is H' = H + 0.1H = 1.1H.
Step 5: The new area of the triangle with the modified base and height is A' = (1/2) * (0.6B) * (1.1H) = 0.33BH.
Step 6: To find the percent change in area:
Percent change = (|A' - A| / A) * 100%
= (|0.33BH - 0.5BH| / (0.5BH)) * 100%
= (0.17BH / (0.5BH)) * 100%
= 34%
Therefore, the percent change in the area of the triangle is 34%.
To find the percent change in the area of the triangle, we need to compare the original area with the new area.
Let's assume the original base of the triangle is "b" and the original height is "h". Therefore, the original area (A1) of the triangle is given by:
A1 = (1/2) * b * h
Now, if the base is decreased by 40%, the new base (b') is equal to 60% of the original base (0.6b). Additionally, if the height is increased by 10%, the new height (h') is equal to 110% of the original height (1.1h).
So, the new area (A2) of the triangle is given by:
A2 = (1/2) * (0.6b) * (1.1h) = (0.33bh)
To find the percent change, we need to calculate the difference between the new area and the original area, divide it by the original area, and then multiply by 100. The formula for percent change is:
Percent Change = ((A2 - A1) / A1) * 100
Plugging in the values, we get:
Percent Change = ((0.33bh - (1/2) * bh) / ((1/2) * bh)) * 100
Simplifying further:
Percent Change = ((0.33 - 0.5) / 0.5) * 100
Percent Change = (-0.17 / 0.5) * 100
Percent Change = -34%
Therefore, the percent change in the area of the triangle is -34%. This signifies a decrease in the area.