# In a figure PQR is a right angled triangle. x and y are the midpoints of PQ and QR respectively. If XY=14 cm,then the hypotenuse PR is?

2
by kunal322

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by kunal322

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The Brainliest Answer!

QX² + QY² = XY² = 14²

[(1/2)QP]² + [(1/2)QR]² = 14²

QP² +QR² = 14²x2²

PR² = (14x2)²

PR = 14x2 = 28

Method 2. Using similarity of triangles

Triangles PRQ and XYQ ar similar.

Hence PR / QR = XY / QY

OR PR = (XY)*(QR/QY) = 14*(2QY/QY) = 28

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See figure.

A line joining the mid points is parallel to the third side. So the triangles PQR and XQY are similar.

XY / PX =PR/PQ

XY / PX = PR / 2 PX

PR = 2 XY = 28 cm

A line joining the mid points is parallel to the third side. So the triangles PQR and XQY are similar.

XY / PX =PR/PQ

XY / PX = PR / 2 PX

PR = 2 XY = 28 cm