Question

the longest side of a triangle is six more units than the shortest side. the third side is twice the length of the shortest side. of the perimeter of the triangle is 25 units, write and solve an equation to find the lengths of all three sides of the triangle.

Answer 1

The lengths of all three sides of the triangle are 4.75 units, 9.5 units and 10.75 units.

Explanation:

Let the longest side of the triangle is a and the shortest side length is c and the intermediate one is b.

So, a > b > c.

Therefore, the perimeter of the triangle will be, a + b + c = 25 ............. (1) {Given}

Now, given that, a = c + 6 .......... (2)

And, b = 2c ............ (3)

Now, from equations (1), (2) and (3), we get

(c + 6) + 2c + c = 25

⇒ 4c = 25 - 6 = 19

⇒ c = 4.75 units.

So, from equation (2) we get,

a = c + 6 = 10.75 units. and

From equation (3) we get,

b = 2c = 9.5 units.

Therefore, the lengths of all three sides of the triangle are 4.75 units, 9.5 units, and 10.75 units. (Answer)