# 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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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.

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

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