Question

Two sides of a triangle have the same length. The third side measures 3 m less than twice that length.the perimeter of the triangle is 21 m. find the lengths of the three sides.

Answer 1

The lengths of three sides are 6 m, 6 m and 9 m.

Explanation:

Given:

Two sides of a triangle have the same length.

The third side measures 3 m less than twice that length.

The perimeter of the triangle is 21 m.

Now, to find the lengths of all three sides.

So, naming the three sides of triangle a, b, and c.

As given two sides of a triangle have the same length.

So, let the first side of triangle(a) be
`x.`

And the other side(b) be same
`x.`

Now, the third side(c) be
`2x-3.`

Perimeter = 21 m.

Now, putting formula to get the sides:

`Perimeter=a+b+c`

`21=x+x+2x-3`

`21=4x-3`

Adding both sides by 3 we get:

`24=4x`

Dividing both sides by 4 we get:

`6=x`

`x=6.`

Now, getting the sides of triangle by putting the value of
`x` :

a = 6 m.

b = 6 m.

c =
`2* 6-3=12-3=9\ m.`

Therefore, the lengths of three sides are 6 m, 6 m and 9 m.