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taurus [48]
3 years ago
13

Find the value of the variable and GH if H is between G and I. GI=5b+2,HI=4b-5, HI=3​

Mathematics
1 answer:
gulaghasi [49]3 years ago
4 0

Answer:

GH = 9 units

Step-by-step explanation:

Given HI = 4b - 5 and HI 3, then

4b - 5 = 3 ( add 5 to both sides )

4b = 8 ( divide both sides by 4 )

b = 2

Thus

GI = 5b + 2 = 5(2) + 2 = 10 + 2 = 12

GH = GI - HI = 12 - 3 = 9

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\large\underline{\sf{Solution-}}

Given that,

In <u>triangle TPQ, </u>

  • RS || PQ,

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As it is given that, <u>RS || PQ</u>

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⇛∠TRS = ∠TPQ [ Corresponding angles ]

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\rm\implies \: \triangle TPQ \:  \sim \: \triangle TRS \:  \:  \:  \:  \:  \:  \{AA \}

<u>Now, We know </u>

Area Ratio Theorem,

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\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{ar( \triangle \: TRS)}  = \dfrac{ {PQ}^{2} }{ {RS}^{2} }

\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15}  = \dfrac{ {6}^{2} }{ {3}^{2} }

\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15}  = \dfrac{36 }{9}

\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15}  = 4

\rm\implies \:ar( \triangle \: TPQ)  = 60 \:  {cm}^{2}

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