Question

the perimeter of the triangular banner is 13 feet. what is the length of the shortest side?
$(x - 5)$ in.
$\frac{x}{2}$ in.
6 in.

• 3 ft
• 4 ft
• 6 ft
• 8 ft

Explanation:

Step1: Convert perimeter to inches

The perimeter is 13 feet. Since 1 foot = 12 inches, we convert 13 feet to inches: \(13\times12 = 156\) inches. Wait, no, wait. Wait, the sides are in inches? Wait, no, the options are in feet. Wait, maybe there's a mistake. Wait, the triangle has sides \((x - 5)\) in, \(\frac{x}{2}\) in, and 6 in. But the perimeter is 13 feet. Wait, that can't be. Wait, maybe the units are mixed? Wait, no, maybe the problem has a typo, but probably the sides are in feet. Let's assume the sides are \((x - 5)\) ft, \(\frac{x}{2}\) ft, and 6 ft. Then the perimeter is the sum of the sides, so \((x - 5)+\frac{x}{2}+6 = 13\).

Step2: Solve the equation for x

Combine like terms: \(x - 5+\frac{x}{2}+6 = 13\) simplifies to \(\frac{3x}{2}+1 = 13\). Subtract 1 from both sides: \(\frac{3x}{2}=12\). Multiply both sides by \(\frac{2}{3}\): \(x = 8\).

Step3: Find the lengths of the sides

Now find each side:

• First side: \(x - 5 = 8 - 5 = 3\) ft.
• Second side: \(\frac{x}{2}=\frac{8}{2}=4\) ft.
• Third side: 6 ft.

Now compare the lengths: 3 ft, 4 ft, 6 ft. The shortest is 3 ft.

Answer:

3 ft