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Sagot :
The original area of the triangle is:
[tex]A_{\text{original}}=243in^2_{}[/tex]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):
[tex]A=\frac{l\times w}{2}[/tex]So for the original triangle:
[tex]\frac{l\times w}{2}=243in^2[/tex]Now, since we are told that the length and width are reduced to 1/3 their orifinal length, the new length is:
[tex]\frac{l}{3}[/tex]And the new width is:
[tex]\frac{w}{3}[/tex]And using this length and width, the area of the new triangle will be calculated as follows:
[tex]A_{\text{new}}=\frac{\frac{l}{3}\times\frac{w}{3}}{2}[/tex]Solving the operations in the numerator:
[tex]\begin{gathered} A_{\text{new}}=\frac{\frac{l\times w}{3\times3}}{2} \\ \\ A_{\text{new}}=\frac{\frac{l\times w}{9}}{2} \end{gathered}[/tex]We can re-write this expression as follows:
[tex]A_{\text{new}}=\frac{1}{9}(\frac{l\times w}{2})[/tex]And we know that for this triangle the expression in parentheses is equal to:
[tex]\frac{l\times w}{2}=243in^2[/tex]Substituting this into the expression to find the new area:
[tex]\begin{gathered} A_{\text{new}}=\frac{1}{9}(243in^2) \\ \\ A_{\text{new}}=27in^2 \end{gathered}[/tex]Answer:
the new area is 27 in^2.
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