Question

A triangle has the following side lengths: x - 2, x, and 3x + 1. Another triangle has the following side lengths: 2x - 5, x + 4, 6x - 7. If the perimeters of the two triangles are equal, what is x?

Answer 1

we know that

Perimeter of a triangle is equal to

P=a+b+c

where

a,b and c are the length sides of the triangle

Find the perimeter of the triangles

Triangle N 1

P=(x-2)+(x)+(3x+1)-------> P=5x-1

Triangle N 2

P=(2x-5)+(x+4)+(6x-7)------> P=9x-8

equate the perimeters

5x-1=9x-8--------> 9x-5x=-1+8-------> 4x=7

x=7/4------> x=1.75

therefore

the answer is

x=1.75