Question

The perimeter of $△$ABC is 18cm. If AB = 5 cm and QR = 7cm, then the length of PQ (in cm) is ___.

Answer 1

In $\Delta ABCand\Delta PQR$,

AB = PR = 5 cm

BC = PQ

AC = QR = 7 cm

$\therefore$ $\Delta ABC\cong \Delta PQR$ by SSS criterion.

Given, perimeter of $△$ABC = 18cm

$\Rightarrow$ AB + AC + BC = 18

Substituting the values of AB and AC, we get,

5+7+BC = 18

$\Rightarrow$ BC = 18 - 5 - 7 = 6 cm

Since BC = PQ, we get PQ = 6 cm