Answer:
The shortest length of the triangle is: 14
Hence, option B is correct.
Step-by-step explanation:
Given the triangle with the lengths
Given that the perimeter of triangle = P = 57
We know that the perimeter of a triangle is the sum of the lengths of the sides of a triangle.
so
[tex]P = (x+15)+(4x-7)+(2x)[/tex]
substitute P = 57
[tex]57 = (x+15)+(4x-7)+(2x)[/tex]
switch sides
[tex]\left(x+15\right)+\left(4x-7\right)+\left(2x\right)=57[/tex]
[tex]x+15+4x-7+2x=57[/tex]
Group like terms
[tex]x+4x+2x+15-7=57[/tex]
Add similar elements
[tex]7x+15-7=57[/tex]
[tex]7x=49[/tex]
divide both sides by 7
[tex]\frac{7x}{7}=\frac{49}{7}[/tex]
simplify
[tex]x=7[/tex]
Now, measuring the lengths by substituting x = 7
- [tex]x+15 = 7+15 = 22[/tex]
- [tex]4x-7 = 4(7)-7 = 28 - 7 = 21[/tex]
- [tex]2x = 2(7) = 14[/tex]
Therefore, the shortest length of the triangle is: 14
Hence, option B is correct.
