Question

in triangle pqr angle r =angle
p. qr =4 CM and pr =5 CM find length of pq

Answer 1

Answer:

Length of pq = 4cm

Step-by-step explanation:

given , angle r = angle p

qr = 4cm , pr = 5cm

since the angle r = angle p

then side qr will be = pq = 4cm

hence, the length of pq = 4cm

Answer 2

The given question is

in triangle pqr angle r =angle p. qr =4 CM and pr =5 CM find length of pq

In triangle if all the angles are equal it is called equilibrium triangle,

If two angles are equal it is called isosceles triangle.

It all the angles are different it is called scalene triangle.

The data given in the question is angle r =angle p.

Assume a triangle PQR

The midpoint of rp is d join qd.

Since,the two angles are equal we get, rD=pD.

In triangle QRD $QR^{2}=rD^{2} +DQ^{2} \\4^{2} =2.5^{2} +DQ^{2} \\DQ^{2} =16-6.25=9.75\\DQ=\sqrt{9.75} =3.1 cm$

Now in triangle PQD

$PQ^{2} = 3.1^{2} + 2.5^{2} \\=9.61+6.25\\=15.86\\3.98 cm\\=4 cm$

IN another method we get

angle r= angle p

qr=4cm

pr=5cm

since the angles r and p are equal we get.

The sides will also be equal  qr=pq,

The length of qr is already given as 4 cm,which means pq is also 4 cm.

Therefore,the final answer is the length of  pq=4cm

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