Question

Suppose $P,$ $Q,$ and $R$ are points in the plane such that $PQ=1.8,$ $PR=8.2,$ and $\angle PQR=90^\circ$. What is the perimeter of $\triangle PQR$?

Answer 1

Perimeter of triangle is 18.

Explanation:

Given:

segment PQ = 1.8

segment PR = 8.2

∠PQR =90°

Since triangle is a right angle triangle with right angle at ∠Q.

Now by using Pythagoras theorem we get;

The square of one side is equal to sum of the square of other two side.

`PQ^2+QR^2 = PR^2`

Substituting the given value we get;

`(1.8)^2+QR^2 = (8.2)^2\\\\3.24+QR^2 = 67.24\\\\QR^2 = 67.24-3.24\\\\QR^2= 64`

Now taking square root on both side we get;

`√(QR^2) =√(64) \\\\QR = 8`

Now we need to find the perimeter of the triangle.

Perimeter of triangle is sum of all three side.

Framing in equation form we get;

Perimeter of triangle = PQ + QR +PR = 1.8 + 8 + 8.2 = 18

Hence Perimeter of triangle is 18.