Question

Two sides of a triangle have the same length. The third side measures m less than twice the common length. The perimeter of the triangle is m. What are the lengths of the three​ sides?

Answer 1

The length of the first side of a triangle = 6 m

The length of the second side of a triangle = 6 m

The length of the third side of a triangle = 9 m

Explanation:

The complete question is: Two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 21 m. What are the lengths of the three​ sides?

We are given that two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 21 m.

Let the common length of the two sides of a triangle be 'x m'.

So, the length of the first side of a triangle = x m

the length of the second side of a triangle = x m

the length of the third side of a triangle = (2x - 3) m

As we know that the perimeter of a triangle is given by;

The Perimeter of a triangle = Sum of all sides of a triangle

21 m = x + x + (2x - 3)

21 m = 2x + 2x - 3

21 m = 4x - 3

4x = 21 + 3

4x = 24 m

x =
`(24)/(4)` = 6 m

Hence, the length of the first side of a triangle = x = 6 m

the length of the second side of a triangle = x = 6 m

the length of the third side of a triangle = (2x - 3) = 12 - 3 = 9 m