Question

Find the value of x in the following figure ...




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Answer 1

${\mathtt{ \underline{ \large{Concept \: used -}}}}$

⚡Here the concept of Pythagoras Therom is used. In this question we have to find the value of x or BC. Two right triangles are given. ∆ BAC have leg of 12 cm and hypotenuse of 13 cm. And in ∆ EDC leg is of length 6 cm and hypotenuse as 10cm.

⚡First find the base of both the triangles using Pythagoras formula and add them. We will get that value of x.

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${\mathtt{ \underline{ \large{Formula \: used }}}}$

${\underline{\boxed{\bold{\orange{hypotenuse² = Leg ²+Base²}}}}}$

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${\mathtt{ \underline{ \large{Solution}}}}$

$\mathtt{Let \: us \: Assume \: ∆ ABC }$

Applying Pythagoras formula

$\to{\bold \color{blue}{AC² =AB² + BC²}}$

$\sf{\implies 13² = 12² + BC²} \\ \\ \sf{\implies 13² - 12² = BC²} \\ \\\sf{\implies 169 -144 = BC²} \\ \\ \sf{\implies 25 = BC²} \\ \\ \sf{\implies\color{red}BC²= 5 cm }$

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$\mathtt{Similarly, \: Let \: us \: assume \: ∆ EDC}$

Applying Pythagoras formula

$\bold{ \to \: { \pink{EC² =ED² + DC²}}}$

$\sf{\implies 10²=6²+DC²} \\ \\ \sf {\implies 100 = 36 + DC²} \\ \\\sf{\implies 100-36 = DC² }\\ \\\sf{\implies 64 = DC²}\\ \\ \sf{\implies \color{lightblue} DC = 8 cm}$

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From the above attached figure we can clearly see that :-

$\bold{ \to \color{green}BC + CD = x}$

so Substitute the value of BC & CD to find the value of x

$\sf{\to X = 8+ 5 }\\ \\ \sf{ \to \: X= 13 cm}$

$\mathtt{\therefore the \: value \: of \: x \: is \: 13 cm.}$

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