Question

1. the rectangle and the triangle shown below have the same perimeter. find the perimeter of the triangle.

rectangle with length ( x + 2 ) and width ( x - 2 ), triangle with sides ( 2x - 8 ), ( 2x - 8 ), and ( x + 6 )

Explanation:

Step1: Calculate rectangle's perimeter

The rectangle has length \( x + 2 \) and width \( x - 2 \). Perimeter of a rectangle is \( 2\times(\text{length} + \text{width}) \), so:

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Step2: Calculate triangle's perimeter

The triangle has sides \( 2x - 8 \), \( 2x - 8 \), and \( x + 6 \). Perimeter of a triangle is the sum of its sides:

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Step3: Set perimeters equal and solve for \( x \)

Since their perimeters are equal:

$$ 4x = 5x - 10 $$

Subtract \( 4x \) from both sides:

$$ 0 = x - 10 $$

So, \( x = 10 \).

Step4: Find triangle's perimeter

Substitute \( x = 10 \) into the triangle's perimeter formula \( 5x - 10 \):

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Answer:

The perimeter of the triangle is \( 40 \).