PQR is an isosceles triangle in which PQ =PR if QR =16cm and the height PM =15cm,calculate PQ

Answer 1

Since triangle PQR is isosceles with PQ = PR, we can conclude that angle PQR = angle PRQ. This means that triangle PQR is also an equilateral triangle.

Since PM is the height of triangle PQR, we can use the height to calculate any side of the equilateral triangle. In an equilateral triangle, the height is also the perpendicular bisector of the base.

Let's call the midpoint of QR as N. So, PN = NM = 8 cm (half of QR)

Now, let's draw line segment PN.

Since triangle PNM is a right-angled triangle with PM as the height, we can use Pythagoras theorem to find PN.

Using Pythagoras theorem:
PN^2 = PM^2 - NM^2
PN^2 = 15^2 - 8^2
PN^2 = 225 - 64
PN^2 = 161
PN ≈ √161 ≈ 12.689 cm

Since triangle PQR is equilateral, PQ = QR = PR.
Therefore, PQ ≈ 12.689 cm.