Question

Given pqr is a right angled triangle, PQ= 16 cm, PR= 8 cm how do you calculate the length of qr?

Answer 1

We have either `QR^2 = PQ^2+PR^2` giving `QR=8 sqrt{5}` or `PQ^2= QR^2 + PR^2` giving `QR=8 sqrt{3}.`

Explanation:

Let's follow the usual convention and call the triangle `PQR` with sides `p=QR, q=PR, r=QP`.

We're given `q=8, r=16` and `PQR` is a right triangle, so one of `P,` `Q,` or `R` is `90^circ.`

`q` isn't the biggest side so can't be the hypotenuse. It's can be either `p` or `r` though. Let's work out both.

`p^2 = q^2 + r^2 = 8^2 + 16^2 = 5(8^2)` so `p= 8 sqrt{5}`

or

`r^2 = p^2 + q^ 2` so `p^2=r^2-q^2=16^2-8^2=3(8^2)` so `p=8 sqrt{3}`.