Question

The perimeter of an isosceles triangle is 15.6m. Find the lengths of its sides, if: b The base is 3m bigger than a leg

Answer 1

The legs are 4.2m long.

The base is 7.2m long.

Explanation:

x=leg

y=base

We can write two equations with the information given.

y=x+3

2x+y=15.6

We can solve this as a system of equations.

y=x+3

-(2x+y=15.6) - make the bottom equation negative.

-2x=x-12.6 - add the bottom to the top, canceling out the y.

-2x+12.6=x - add 12.6 to both sides.

12.6=3x - add 2x to both sides.

4.2=x - divide both sides by 3.

x=4.2

Now we can solve for y.

y=x+3

y=(4.2)+3 - substitute in the x.

y=7.2

Answer 2

Length of an isosceles triangle is, 3.12 m

Explanation:

Given: Perimeter of an isosceles triangle is 15.6 m.

Let a be the length of sides and b be the base of an isosceles triangle respectively.

To find the length of the sides(a);

Isosceles triangle is a triangle with two equal sides and two equal base angles.

Perimeter of the isosceles triangle is the sum of the three sides i,e

Perimeter(P) = a +b +a = 2a +b

also it is given that; the base is 3 m bigger than a leg.

⇒ b = 3 a

Substitute this in perimeter formula;

P = 2a +3a =5a

Substitute the value of perimeter = 15.6 m

we have;

`15.6 = 5a`

Divide both sides by 5 we get;

`(15.6)/(5) = (\5a)/(5)`

Simplify;

a = 3.12 m

Therefore, the length of the sides of an isosceles triangle is, 3.12 m