Question

In an isosceles triangle PQR, the length of equal sides PQ and PR is 13 cm and base QR is 10 cm. Find the length of perpendicular bisector drawn from vertex P to side QR.

Answer 1

Given: In an isosceles triangle PQR, PQ = PR = 13 cm and base QR = 10 cm.

Since, PS is the perpendicular bisector,

∴ QS = SR = `(QR)/2 = 10/2` = 5

Now, using Pythagoras' theorem, in a right-angled triangle PSQ,

PS² + SQ² = PQ²

Substituting the values of SQ and PQ in equation (i),

PS² + 5² = 13² 

⇒ PS² = 13² – 5²

⇒ PS² = 169 – 25

⇒ PS² = 144

∴ PS = `sqrt(144)` = 12

As a result, the length of the perpendicular bisector PS is 12 cm.