Question

look at this triangle: if both dimensions are quadrupled, then which of the following statements about its area will be true? the new area will be 16 times the old area. the new area will be 1/4 of the old area. the new area will be 9 times the old area. the new area will be 4 times the old area.

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.

Step2: Consider the effect of quadrupling dimensions

If the base $b$ becomes $4b$ and the height $h$ becomes $4h$, then the new - area $A_{new}=\frac{1}{2}(4b)(4h)$.

Step3: Simplify the new - area formula

$A_{new}=\frac{1}{2}(4b)(4h)=16\times\frac{1}{2}bh$. Since $A = \frac{1}{2}bh$ (original area), the new area is 16 times the old area.

Answer:

The new area will be 16 times the old area.