Question

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On the left triangle, the shorter side is labeled 4 inches and the longer side is labeled 10 inches. On the right triangle, the shorter side is labeled x inches and the longer side is labeled 20 inches.

The two triangles above are similar. Find the value of x. Be sure to explain your steps.

Answer 1

8

Explanation:

We are dealing with similaraty and similar shapes length are in proportion so we are going to set up an proportion.

Length of left triangle small side/ Length of left triangle long side= length of right triangle small side/length of right triangle long side

4/10=x/20

Cross multiply: 10x=80

x=8

Answer 2

• x = 8 inches

Explanation:

As the triangles are similar, their corresponding sides will have same ratio:

• left short side /right short side = left long side / right long side

or simpler

• s₁/s₂ = l₁/l₂

Substitute values to find the missing one:

• 4/x = 10/20
• 4/x = 1/2
• x = 4*2
• x = 8

The missing side is 8 inches long