Question

describe how the given changes to the dimensions of the figure will affect its perimeter or area. what happens to the area of a triangle with base 12 units and height 7 units when its dimensions are increased by a factor of 3? > move an answer into each space provided. the area of the resulting triangle will be than the area of the original triangle. 3 more 9 more 3 times greater 9 times greater

Explanation:

Step1: Recall area formula for triangle

The area formula of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. For the original triangle with $b = 12$ and $h=7$, the original area $A_1=\frac{1}{2}\times12\times7 = 42$.

Step2: Find new dimensions

The dimensions are increased by a factor of 3. So the new base $b_2=12\times3 = 36$ and the new height $h_2=7\times3=21$.

Step3: Calculate new - area

The new area $A_2=\frac{1}{2}\times b_2\times h_2=\frac{1}{2}\times36\times21$.
$A_2=\frac{1}{2}\times36\times21 = 378$.

Step4: Find the ratio of new area to original area

$\frac{A_2}{A_1}=\frac{378}{42}=9$.

Answer:

9 times greater