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A triangle with a perimeter of 43 units is the image of a triangle that was dilated by a scale factor of
(4)/(3). Find the perimeter of the preimage, the original triangle, before its dilation. Round your answer to the nearest tenth, if necessary.
Answer: units

A triangle with a perimeter of $43$ units is the image of a triangle that was dilated by a scale factor of $\frac{4}{3}$ . Find the perimeter of the preimage, the original triangle, before its dilation. Round your answer to the nearest tenth, if necessary. $\newline$ Answer: units

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Scale drawings: word problems

Full solution

Q. A triangle with a perimeter of

43

units is the image of a triangle that was dilated by a scale factor of

\frac{4}{3}

. Find the perimeter of the preimage, the original triangle, before its dilation. Round your answer to the nearest tenth, if necessary.

\newline

Answer: units

Calculate Scale Factor: To find the perimeter of the original triangle before dilation, we need to use the scale factor that was applied to the triangle to get the dilated image. The scale factor given is $(4)/(3)$ , which means that every length in the original triangle was multiplied by $(4)/(3)$ to get the dilated triangle.
Find Perimeter of Original Triangle: The perimeter of the dilated triangle is given as $43$ units. To find the perimeter of the original triangle, we need to divide the perimeter of the dilated triangle by the scale factor. $\newline$ Calculation: Perimeter of original triangle $=$ Perimeter of dilated triangle $/$ Scale factor $\newline$ Perimeter of original triangle $= 43$ units $/$ $(4/3)$
Perform Division: Perform the division to find the perimeter of the original triangle. $\newline$ Calculation: Perimeter of original triangle = $43$ units $\times \left(\frac{3}{4}\right)$ $\newline$ Perimeter of original triangle = $\frac{129}{4}$ $\newline$ Perimeter of original triangle = $32.25$ units
Round to Nearest Tenth: Since the problem asks to round the answer to the nearest tenth if necessary, we round $32.25$ to $32.3$ units.

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