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the triangles are similar. the area of the larger triangle is 1583 ft². Find the area of the smaller triangle to the nearest square foot

The Triangles Are Similar The Area Of The Larger Triangle Is 1583 Ft Find The Area Of The Smaller Triangle To The Nearest Square Foot class=

Sagot :

Answer:

223 ft²

Explanation:

First, we need to find the scale factor. So, taking into account the lengths of the triangles, we get that the scale factor is:

[tex]k=\frac{15\text{ ft}}{40\text{ ft}}=0.375[/tex]

Then, to know the area of the smaller triangle, we will use the following equation:

[tex]A_{2\text{ }}=k^2(A_1)[/tex]

Where A2 is the area of the smaller triangle and A1 is the area of the larger triangle.

So, replacing k by 0.375 and A1 by 1583 ft², we get that the area of the smaller triangle is equal to:

[tex]\begin{gathered} A_2=(0.375)^2(1583) \\ A_2=(0.1406)(1583) \\ A_2=222.6\approx223ft^2 \end{gathered}[/tex]

Therefore, the answer is 223 ft²

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