nicekikah
2021-08-03
Answered

Given $\mathrm{\u25b3}ABC\sim \mathrm{\u25b3}QRS$ what is the value of x?

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hosentak

Answered 2021-08-04
Author has **100** answers

Given that $\mathrm{\u25b3}ABC\sim \mathrm{\u25b3}QRS$

by the corresponding part of similar triangles

$\Rightarrow \mathrm{\angle}A=\mathrm{\angle}Q,\mathrm{\angle}B=\mathrm{\angle}R\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\mathrm{\angle}C=\mathrm{\angle}S$

now in$\mathrm{\u25b3}ADC\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\mathrm{\u25b3}QPS$

here$\mathrm{\angle}ADC=\mathrm{\angle}QPS$ (each $90}^{\circ$ )

$\mathrm{\angle}C=\mathrm{\angle}S$ (from above)

using angle angle similarity criteria of triangle

$\mathrm{\u25b3}ADC\sim \mathrm{\u25b3}QPS$ (by angle angle similarity)

by the corresponding part of similar triangles

$\frac{SQ}{CA}=\frac{AD}{QP}$

$\Rightarrow \frac{x}{18}=\frac{10}{12.5}$

$\Rightarrow x=\frac{10\times 18}{12.5}=14.4$

$\Rightarrow x=14.4$

this is the required answer.

by the corresponding part of similar triangles

now in

here

using angle angle similarity criteria of triangle

by the corresponding part of similar triangles

this is the required answer.

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