The area of a triangle is 243 in. If both its length and width are reduced to one- third their original length, what would its new area be?

Question

asked Jan 13, 2023 142k views

1 Answer

Mark Bao · Answer 1 · 2023-01-20T02:52:50+0000

The original area of the triangle is:

$A_{\text{original}}=243in^2_{}$

Let's call the original length "l" and the original width "w".

And now we remember the formula to calculate the area of a triangle using the length (or base) and the width (or height):

So for the original triangle:

Now, since we are told that the length and width are reduced to 1/3 their orifinal length, the new length is:

And the new width is:

And using this length and width, the area of the new triangle will be calculated as follows:

$A_{\text{new}}=((l)/(3)*(w)/(3))/(2)$

Solving the operations in the numerator:

$\begin{gathered} A_{\text{new}}=((l* w)/(3*3))/(2) \\ \\ A_{\text{new}}=((l* w)/(9))/(2) \end{gathered}$

We can re-write this expression as follows:

$A_{\text{new}}=(1)/(9)((l* w)/(2))$

And we know that for this triangle the expression in parentheses is equal to:

Substituting this into the expression to find the new area:

$\begin{gathered} A_{\text{new}}=(1)/(9)(243in^2) \\ \\ A_{\text{new}}=27in^2 \end{gathered}$

Answer:

the new area is 27 in^2.