Answered: "In the diagram of △GKJ below, LH∥KJ, GL=4,..."

High School
Geometry
High school geometry
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facas9

Answered question

2021-08-08

In the diagram of $△ G K J$ below, $L H ∥ K J$ , GL=4, LK=24, and HJ=30. What is the lenght of GJ?

Answer & Explanation

mhalmantus

Skilled2021-08-09Added 105 answers

Step 1
Here, the objective is to find the length of the side using the similarity of the triangle.
Step 2
In the figure, check the similarity of the triangles $△ G L H and △ G K J$ .
Here, $L H ∥ K J$ , therefore,
$∠ G L H = ∠ G K J$
$∠ G H L = ∠ G J K$
$∠ L G H = ∠ K G J$
Therefore, both the triangles $△ G L H \approx △ G K J$
So, the ratio of sides of the triangles will be equal.
Step 3
Now, use the ratio of the sides as,
$\frac{G L}{L K} = \frac{G H}{H J}$
$\frac{4}{24} = \frac{G H}{30}$
GH=5
The length of the side GJ is,
GJ=GH+HJ
=5+30
=35
Therefore, the length of side GJ=35

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