Video: Finding the Base Length of a Trapezium given the Other Baseโ€™s Length and the Middle Baseโ€™s Length

In the figure, ๐ฟ๐ป is the midsegment of trapezoid ๐น๐บ๐ฝ๐พ. What is the value of ๐‘ฅ?

02:23

Video Transcript

In the figure, ๐ฟ๐ป is the midsegment of trapezoid ๐น๐บ๐ฝ๐พ. What is the value of ๐‘ฅ?

So we have a diagram of a trapezoid. And weโ€™re told that the line segment ๐ฟ๐ป is its midsegment. What does this is mean? Firstly, the midsegment of a trapezoid is parallel to each base. So in this case, thatโ€™s the lines ๐น๐บ and ๐พ๐ฝ.

Secondly, the midsegment connects the midpoints of the legs of the trapezoid. We can see the ๐ฟ and ๐ป are the midpoints of the two legs because the line segments ๐น๐ฟ and ๐ฟ๐พ are equal in length and also the line segments ๐บ๐ป and ๐ป๐ฝ are equal to each other in length.

Weโ€™ve been told the length of one of the bases of the trapezoid ๐พ๐ฝ and the length of the midsegment. The value weโ€™re looking to calculate, ๐‘ฅ, is the length of the second base of the trapezoid ๐น๐บ.

In order to answer this question, we need to recall the trapezoid midsegment theorem. It tells us this. The measure of the midsegment of a trapezoid is half the sum of the lengths of the bases. In this trapezoid, the bases are 23.6 and ๐‘ฅ. The length of the midsegment is 18.6. So we can express this as an equation. Half the sum of the length of the bases, so thatโ€™s ๐‘ฅ plus 23.6 over two, is equal to 18.6.

To find ๐‘ฅ, we now need to solve this equation. The first step is to multiply both sides of the equation by two. This gives ๐‘ฅ plus 23.6 is equal to 37.2. The final step in solving this equation is to subtract 23.6 from both sides. This gives ๐‘ฅ is equal to 13.6. So we found the value of ๐‘ฅ. Itโ€™s 13.6.

Remember, the key fact we used in this question was the trapezoid midsegment theorem, which tells us that the measure of the midsegment of a trapezoid is half the sum of the lengths of the bases.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.