Question

The length of the base of an isosceles triangle is x.The length of a leg is 3x - 5. The perimeter of the triangle is 25. Find x.

Answer 1

So, the value of x is 5.

Explanation:

To find the value of x in an isosceles triangle with a base of x and legs of 3x - 5, you can use the formula for the perimeter of a triangle, which is:

Perimeter = Sum of all sides

In this case, the perimeter is given as 25, and the sum of all sides includes the base (x) and both legs (3x - 5 and 3x - 5).

So, you can set up the equation:

25 = x + (3x - 5) + (3x - 5)

Now, simplify and solve for x:

25 = x + 3x - 5 + 3x - 5

Combine like terms:

25 = 7x - 10

Now, add 10 to both sides of the equation to isolate 7x:

25 + 10 = 7x

35 = 7x

Finally, divide both sides by 7 to find the value of x:

x = 35 / 7

x = 5

So, the value of x is 5.

Answer 2

x = 5

Explanation:

In geometry, an isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs, and the third side is called the base. The angles opposite the legs are called the base angles, and the angle opposite the base is called the vertex angle.

In this case:

Let the isosceles triangle be ABC, with AB = AC = 3x - 5 and BC = x.

The perimeter of the triangle is the sum of the lengths of the three sides:

AB + AC + BC = Perimeter

We have Perimeter = 25

Substituting the known values, we get:

(3x - 5) + (3x - 5) + x = 25

Combining like terms, we get:

7x - 10 = 25

Adding 10 to both sides, we get:

7x - 10 + 10 = 25 + 10

7x = 35

Dividing both sides by 7, we get:

`\sf (7x)/(7) =(35)/(7)`

x = 5

Therefore, the value of x is 5.

We can also find the value of other side by substituting value of x.

Length of base = x = 5

Length of leg = 3x - 5 = 3 × 5 - 5 = 15 - 5 = 10