The area of an equilateral triangle is decreased to 9/16 of its original amount. How does its new area compare to its original area?
You already stated the answer.
It is 9/16 of its original area.
You probably meant to ask:
How do the sides of the reduced triangle compare to the original sides?
Remember what I told you in a question similar to this?
"The area of similar shapes is proportional to the square of their corresponding sides"
area of new : area of original = side^2 of new : side^2 of old
= 9/16
= 3^2 / 4^2
so the new side is 3/4 of the old side
No this was the exact question in my textbook
To determine how the new area of the equilateral triangle compares to its original area, we first need to find the ratio between the new area and the original area.
Let's denote the original area of the equilateral triangle as A_0 and the new area as A_1. We are given that A_1 is 9/16 of A_0.
Therefore, we can write the following equation:
A_1 = (9/16) * A_0
To compare the new area to the original area, we express A_1 / A_0:
(A_1 / A_0) = [(9/16) * A_0] / A_0
Simplifying, we get:
(A_1 / A_0) = 9/16
So the new area of the equilateral triangle is 9/16 of its original area.
In conclusion, the new area of the equilateral triangle is smaller than its original area, as it has decreased by a factor of 9/16.