Question

. In ∆PQR, points X, Y, Z are the midpoints of side PQ, side QR and side PR, respectively. If PQ = 6 cm, QR = 10 cm and PR = 12 cm, find the length of XY, YZ and XZ.​

Answer 1

Step-by-step explanation:

The area of the triangle xyz is 48 cm²

Step-by-step explanation:

In the triangle xyz , p.q,r are the midpoints on the side of side xy,yz,zy

the area of traingle pqr = 12 sq. cm (given)

we have to find the area of triangle xyz

as, the traingle formed by joining the midpoints of the sides of the triangle is one forth of the traingle

using this

area of triangle pqr = one forth of area of triangle xyz

i.e

area(\bigtriangleup (pqr)△(pqr) )=\frac{1}{4}

4

1

area(\bigtriangleup (xyz)△(xyz) )

putting the value from of area of traingle pqr

12=\frac{1}{4}

4

1

area(\bigtriangleup (xyz)△(xyz) )

12\times 4=area(xyz)12×4=area(xyz)

48=area(xyz)

hence,

the area of the triangle xyz is 48 cm²

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