✎ Problem:

A sign board is in the shape of an isosceles triangle. The third side measures 3 feet less than twice the length of the other two sides. Find the length of the sides of the sign board if the perimeter is 61 feet.

✎ Answer and explanation:

Let

• x be the length of the first and second sides since the triangle is isosceles, and
• 2x - 3 be the length of the third side.

Since the perimeter is equal to 61 ft, we can make an equation to solve for x:

• (2x - 3) + x + x = 61
• 4x - 3 = 61
• 4x = 64
• ∴ x = 16 ft <length of the first and second sides>

The length of the first and second sides are x = 16 ft. Now we have to solve for the third side:

• 2x - 3
• 2 (16) - 3
• 32 - 3 → 29 ft <length of the third side>

✔︎ Let's see if these values add up to the perimeter of the triangle, which is 61 ft.

• 29 ft + 16 ft + 16 ft ≟ 61 ft
• 45 ft + 16 ft ≟ 61 ft
• 61 ft = 61 ft

Hope This Helps

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