To determine:To Find:the measure of side VC in the figure shown such that VA' = 15, A'A=20 and VC'=18 Given: Figure is shown below. 12210202971.jpg

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asked 2021-01-15
To determine:To Find:the measure of side VC in the figure shown such that VA' = 15, A'A=20 and VC'=18
Given:
Figure is shown below.
image

Answers (1)

2021-01-16
Calculation:
Since, plane of \(\displaystyle\triangle{A}'{B}'{C}'\) is similar to the plane of \(\displaystyle\triangle{A}{B}{C}\)
Since, ABCD is a parallelogram.
\(\displaystyle\angle{B}=\angle{V}\therefore\)(Common)
\(\displaystyle\angle{V}{A}{B}=\angle{V}{A}'{B}'\therefore\)(Corresponding angle in two similar plane)
Therefore by AA similarity, \(\displaystyle\triangle{V}{A}{B}\sim\triangle{V}{A}'{B}'\)
Ratio of corresponding sides in two similar triangles is equal.
\(\displaystyle\frac{{{V}{A}}}{{{V}{A}'}}=\frac{{{V}{C}}}{{{V}{C}'}}\)
\(\displaystyle\frac{{{V}{A}'+\forall'}}{{{V}{A}'}}=\frac{{{V}{C}}}{{{V}{C}'}}\)
\(\displaystyle\frac{{{15}+{20}}}{{{15}}}=\frac{{{V}{C}}}{{{18}}}\)
\(\displaystyle{V}{C}=\frac{{{18}\times{35}}}{{{15}}}\)
VC=42
Therefore, the answer is 42.
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