Question

if triangle ABC similar to triangle PQR, perimeter of triangle ABC=32cm and perimeter of triangle PQR =48cm and PR=6cm then the length of AC is equal to​

Answer 1

Let us assume two similar triangles as ΔABC ∼ ΔPQR. Let AD and PS be the medians of these triangles.

ΔABC ∼ ΔPQR

…(1)

∠A = ∠P, ∠B = ∠Q, ∠C = ∠R … (2)

Since AD and PS are medians,

∴ BD = DC =

And, QS = SR =

Equation (1) becomes

… (3)

In ΔABD and ΔPQS,

∠B = ∠Q [Using equation (2)]

And, [Using equation (3)]

∴ ΔABD ∼ ΔPQS (SAS similarity criterion)

Therefore, it can be said that

… (4)

From equations (1) and (4), we may find that

And hence,