Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
