221k views
4 votes
In an isosceles triangle, the length of each leg exceeds twice the base by 2cm. Perimeter is 24. How long is each leg?

User Rouliboy
by
8.0k points

2 Answers

4 votes

Answer:

Each leg 10 units in length.

Explanation:

Since this is an isosceles triangle, both sides are equal which means we can set up a system of equations for this, l will symbolize the legs and b will symbolize the base.

2l+b=24 This equation means that the length of 2 legs and the base will add up to 24.

l=2b+2 This equation means that the length of one leg added to 2 is equal to twice the base.

Now, solve the system, I will use substitution.

Next, substitute the 2nd equation into the first to solve for b.

2(2b+2)+b=24, Solve for b:

4b+4+b=24

5b= 20

b=4, This means that the length of the base is 4, now solve for the length of each leg using either of the equations by plugging in the value of b.

l=2(4)+2

l=10, The length of each leg is 10

User Jepio
by
8.0k points
3 votes
if the base is x cm, the leg will be (2x+2) cm.
2(2x+2)+x=24
4x+4=24
4x=20
x=5 cm
So, the base is 5cm
leg: 2*5+2=12 cm
So, the length of each leg is 12 cm
User Xzin
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.