Mathematics: The scale factor of the dimensions of two similar wood floors is 5 : 4. it costs $368 to refinish the smaller wood floor.

The scale factor of the dimensions of two similar

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FireStorm7327

17.09.2021

Mathematics

The answer is below

Step-by-step explanation:

Two triangles are said to be similar if the ratio of their corresponding sides are equal.

From the problem, since GRPC is a parallelogram, hence:

GC is parallel to RE and GR is parallel to CP.

∠GBC = ∠EBP (vertical opposite angles are equal)

∠BGC = ∠BEP (alternate interior angles are equal)

∠BCG = ∠BPE (alternate interior angles are equal)

Since, ∠GBC = ∠EBP, ∠BGC = ∠BEP and ∠BCG = ∠BPE, we can say that triangle BCG is similar to triangle BEP by the angle - angle - angle similarity postulate.

c) Since the triangle BCG is similar to triangle BEP, hence:

$\frac{BC}{BP} =\frac{BG}{BE} =\frac{CG}{PE} \\\\using\ \frac{BC}{BP} =\frac{BG}{BE} \\\\\frac{350}{250} =\frac{450}{BE} \\\\BE=\frac{450*250}{350} =321.4\ feet\\\\using\ \frac{BC}{BP} =\frac{CG}{PE} \\\\\frac{350}{250} =\frac{400}{PE} \\\\PE=\frac{250*400}{350}=285.7\ feet$

Part A: Identify a pair of similar triangles. (2 points) Part B: Explain how you know the triangles

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The scale factor of the dimensions of two similar wood floors is 5 : 4. it costs $368 to refinish the smaller wood floor.

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