Question

look at this triangle: if both dimensions are tripled, then which of the following statements about its area will be true? the new area will be 3 times the old area. the new area will be 1/4 of the old area. the new area will be 4 times the old area. the new area will be 9 times the old area.

Explanation:

Step1: Recall triangle - area formula

The area formula of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Let the original base be $b_1$ and height be $h_1$, original area $A_1$

$A_1 = \frac{1}{2}b_1h_1$.

Step3: New base $b_2 = 3b_1$ and new height $h_2=3h_1$, find new area $A_2$

$A_2=\frac{1}{2}b_2h_2=\frac{1}{2}(3b_1)(3h_1)=9\times\frac{1}{2}b_1h_1$.

Step4: Compare new and old areas

Since $A_2 = 9A_1$, when both dimensions are tripled, the new area will be 9 times the old area.

Answer:

The new area will be 9 times the old area.