Answer:
The value of x is 4
The lengths of the sides of the triangle are 4 ft, 8 ft, and 5 ft
Step-by-step explanation:
The perimeter of the triangle is the sum of the lengths of its three sides
In the given figure
∵ The perimeter of the triangle is 17 feet
∵ The length of its sides are x ft, 2x ft, and 5 ft
∵ P = s1 + s2 + s3
→ Substitute the values of the three sides and the perimeter in the equation
∴ 17 = x + 2x + 5
→ Add the like terms on the right side
∵ 17 = 3x + 5
→ Subtract 5 from both sides
∴ 17 - 5 = 3x + 5 - 5
∴ 12 = 3x
→ Divide both sides by 3 to find x
∵ [tex]\frac{12}{3}[/tex] = [tex]\frac{3x}{3}[/tex]
∴ 4 = x
∴ The value of x is 4
→ Use the value of x to find the length of each side
∵ s1 = x
∴ s1 = 4 ft
∵ s2 = 2x
∴ s2 = 2(4)
∴ s2 = 8 ft
∴ The lengths of the sides of the triangle ar 4 ft, 8 ft, and 5 ft
