Question

r is the midpoint of op and qr is perpendicular to op in the diagram below find the the length of qr

Answer 1

Given:

OP = 20 in

QP = 26 in

Since R is the midpoint of OP, then, OR = RP

Thus

`OR=RP=(OP)/(2)=(20)/(2)=10\text{ in}`

To find the length of QR, use pythagoras theorem below:

`\begin{gathered} a^2+b^2=c^2 \\ \\ RP^2+QR^2=PQ^2 \end{gathered}`

Input values into the formula:

`10^2+QR^2=26^2`

Subtract 10² from both sides:

`\begin{gathered} 10^2-10^2+QR^2=26^2-10^2 \\ \\ QR^2=26^2-10^2 \end{gathered}`

Take the square root of both sides:

`\begin{gathered} \sqrt[]{QR^2}=\sqrt[]{26^2-10^2} \\ \\ QR=\sqrt[]{676-100} \\ \\ QR=\sqrt[]{576} \\ \\ QR=24 \end{gathered}`

Therefore, the length of QR is 24 in