Question

Triangle ABC congruent to triangle PQR. BC = 6.5 cm and QR = 10.4 cm and perimeter of triangle PQR = 96cm. Then the perimeter of triangle ABC.​

Answer 1

perimeter of triangle ABC is also 96cm as both triangles are congruent

Answer 2

If ∆ABC ≅ ∆PQR, BC = 6.5 cm, QR = 10.4 cm and perimeter of ∆PQR = 96 cm then the perimeter of ∆ABC is 60 cm.

Step-by-step explanation:

Hi there,

It is given in the question that the triangles are congruent to each other and the measurement of sides are given differently. If two triangles are congruent then their sides are always the same length by CPCT theorem. So considering the triangles to be similar to each other instead and solving it accordingly.

It is given that,

∆ABC ~ ∆PQR

BC = 6.5 cm

QR = 10.4 cm

Perimeter of ∆PQR = 96 cm

Since ∆ABC ~ ∆PQR, so, we know that when two triangles are similar to each other then the ratio of their perimeters are equal to the ratio of their corresponding sides i.e.,

[Perimeter of ∆ABC] / [Perimeter of ∆PQR] = [AB/PQ] = [BC/QR] = [AC/PR] ….. (i)

Therefore, by substituting the given values in (i), we get

[Perimeter of ∆ABC] / 96 = [6.5/10.4]  

⇒ [Perimeter of ∆ABC] = [6.5/10.4]  × 96

⇒ [Perimeter of ∆ABC] = 0.625 × 96

⇒ Perimeter of ∆ABC = 60 cm

Thus, the perimeter of the triangle ABC is 60 cm.

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