Question

∆PQR is right angled at Q. A and B are the mid-points of sides PQ and PR respectively. If PQ=10 cm and PR=26 cm, then find the length of AB

Answer 1

OK so by using the mid point theorem...AB=1/2QR and also AB||QR..so Angle PAB=90°(alternate angles)..so in Triangle PAB..PA=10/2=5cm and PB=26/2=13cm..so by using Pythagoras theorem=>AB^2=PB^2-PA^2=169-25=144=AB^2... so AB=12cm(ans)

Answer 2

Given,

∆ PQR is right-angled at Q.

A and B are the mid-points of sides PQ and PR respectively.

PQ=10 cm and PR=26 cm

To find,

The length of AB.

Solution,

The length of AB will be 12 cm.

We can easily solve this problem by following the given steps.

According to the question,

∆ PQR is right-angled at Q.

A and B are the mid-points of sides PQ and PR respectively.

PQ=10 cm and PR=26 cm

AP = 10/2 cm = 5 cm

AP = 10/2 cm = 5 cmPB = 26/2 cm = 13 cm --- (mid-points)

When ∆ PQR is right-angled at Q then ∆ PAB will also be right-angled at A.

Using Pythagoras theorem in ∆PAB,

PB² = AP²+AB²

AB² = PB²-AP²

AB² = (13)²-(5)²

AB² = 169-25

AB² = 144

AB = √144

AB = 12 cm

Hence, the length of AB is 12 cm.