Question Video: Properties of Rectangles in a Real-World Context | Nagwa Question Video: Properties of Rectangles in a Real-World Context | Nagwa

# Question Video: Properties of Rectangles in a Real-World Context

A rectangular park has two walking paths as shown. If ππ = 100 m and ππ = 213 m, find the length of line segment ππ.

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### Video Transcript

A rectangular park has two walking paths as shown. If ππ equals 100 metres and ππ equals 213 metres, find the length of line segment ππ.

Letβs have a look at this rectangle and fill in the lengths that weβre given. Weβre told that ππ is 100 metres and ππ 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 ππ, which is marked in blue on the diagram. Notice that the line ππ and the line ππ are the diagonals of the rectangle. So letβs 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 theyβre 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 ππ is equal to the other diagonal ππ, since they are congruent. And therefore theyβre both 213 metres. And so to find the length of ππ, we know that since our diagonals bisect each other, then this is equal to half of the length ππ. So we find half of 213 which is 106.5 metres. So our answer for the length of ππ is 106.5 metres. In this question, we were given the information that ππ is 100 metres which we didnβt need to use. This is common in exam questions to distract us from the information that we do need to use.

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