Question

Given: KLMN is a trapezoid, KL=MN, AB is a midsegment, AB=18, KL=15, LM:KN=1:5 Find: h

Answer 1

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Answer 2

The height LC or h of trapezium KLMN is 9.

It is given that

KL = 15

AB = 18

LM:KN = 1:5

KL = MN

Since we know that the mid-segment of a trapezoid is half of the sum of parallel sides.

i.e. 18 = (LM+KN)/2

LM+KN = 36

Since, LM: KN = 1:5

Let us assume LM and KN as x and 5x respectively.

x+5x =36

6x =36

x=6

So, LM = 6

KN = 30

Find the attached diagram to visualize better.

What is isosceles trapezium?

A trapezium in which non-parallel sides are equal called isosceles trapezium.

Since, LK = MN, This means LMKN is an isosceles trapezium

So, KC =ND

KC +ND + LM = 30

KC +KC + 6 = 30

2KC = 24

KC =12.

So, using Pythagoras Theorem

In triangle LKC

KL²=LC²+KC²

LC²=KL²-KC²

LC² = 15²-12²

LC² = 81

LC =9 =height h

Therefore, The height LC or h of trapezium KLMN is 9.

To get more about trapezium visit:

https://brainly.com/question/314251