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Find the perimeter of the following isosceles triangle. show work

Find the perimeter of the following isosceles triangle. show work-example-1

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Answer

Find out the perimeter of the isosceles triangle.

To prove

As shown in the figure.

P(0,4) , Q(-2,0) and R(2,0) are the vertices of the triangle PQR.

Formula


Distance\ formula = \sqrt{(x_(2) - x_(1))^(2) +(y_(2) -y_(1))^(2)}

As P(0,4) and Q(-2,0)


PQ = \sqrt{(-2 - 0)^(2) +(0 - 4)^(2)}


PQ = √(4+16)


PQ = √(20)\unit

In the isoceles triangle the two sides of the triangles are equal .

Therefore PQ = PR


PR = √(20)\unit

As Q(-2,0) and R(2,0)


QR = \sqrt{(2- (-2))^(2) +(0 - 0)^(2)}


QR = \sqrt{(4)^(2)}

QR = 16 unit


Perimeter\ of\ triangle PQR = √(20) +√(20) + 16


Perimeter\ of\ triangle PQR = 4√(5) + 16\ units^(2)


User Kirill Shlenskiy
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