### Video Transcript

A rectangular park has two walking paths as shown. If ππ equals 100 metres and ππ
equals 213 metres, find the length of line segment ππ.

Letβs have a look at this rectangle and fill in the lengths that weβre given. Weβre told that ππ is 100 metres and ππ
is 213 metres. it might be very tempting at this point to look at our values and think we may have to use the Pythagorean theorem, since we did after all have 90-degree angles in this rectangle. However, this question is asking us to find the length of ππ, which is marked in blue on the diagram. Notice that the line ππ
and the line ππ are the diagonals of the rectangle. So letβs see if we can use any facts about the diagonals of the rectangle to help.

We can recall that the diagonals of a rectangle are congruent, which means that theyβre exactly the same length. They also bisect each other, which means that each diagonal cuts the other one into two identical length pieces. So if we look at our rectangle, then the diagonal ππ is equal to the other diagonal ππ
, since they are congruent. And therefore theyβre both 213 metres. And so to find the length of ππ, we know that since our diagonals bisect each other, then this is equal to half of the length ππ. So we find half of 213 which is 106.5 metres. So our answer for the length of ππ is 106.5 metres. In this question, we were given the information that ππ is 100 metres which we didnβt need to use. This is common in exam questions to distract us from the information that we do need to use.