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

1 Answer
Apr 25, 2018

Answer:

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}#.