Question

Shown below is triangle ABC. Calculate the perimeter of the triangle.

Answer 1

$\huge\sf\underline{\underline{Given \ratio \: - }}$

•P = (1,2)

•Q = (1,6)

•R = (-4,2)

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$\huge\sf\underline{\underline{to \: find \ratio \: - }}$

Prove that PQR is a traingle

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$\huge\sf\underline{\underline{formula \ratio \: - }}$

$\boxed{ \sf { d = \sqrt{ (x1 - x2 )² +( y1 - y2)²}}}$

$\boxed{ \sf \: Hypotenuse² = Base² + Altitude ²}$

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$\huge\sf\underline{\underline{answer \ratio \: - }}$

By applying the formula ,

$\boxed{ \sf { d = \sqrt{ (x1 - x2 )² +( y1 - y2)²}}}$

• PQ = √[(1-1)²+(2-6)²]

= √[(16)]

= 4

PR = √[(1-(-4))²+(2-2)²]

= √[5²]

= 5

RQ = √[(-4-1)²+(2-6)²]

= √[25+16]

= √[41]

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According to Pythagorean theorem ,

$\boxed{ \sf \: Hypotenuse² = Base² + Altitude ²}$

• consider LHS ,

• Hyp² = √[41]²

= 41

• Now RHS ,

• base ² + alt ² = 4² + 5²

= 16 + 25

= 41

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Since LHS = RHS ,

it can be concluded that this is a right traingle