The base of an isosceles triangle is 5 and it's perimeter is 11. the base of a similar isosceles triangle is 10.what is the perimeter of the larger triangle

the perimeter of the larger triangle is 22 units

Step-by-step explanation:

The diagram of both triangles is shown in the attached photo. The isosceles triangles are triangle ABC and triangle DEF

Perimeter of triangle ABC = 11

For an isosceles triangle, the other two sides are equal. If one equal side is x, then the sum of the two equal sides is x+x = 2x

Perimeter of triangle = sum of the lengths of the 3 sides. Therefore,

11 = 5 + 2x

2x = 11-5 = 6

x = 6/2 = 3

The base of the similar triangle is 10. It means that it is 2 times the base of the smaller triangle. That means the scale factor is 2. Therefore,

If the perimeter of the small triangle is 11, the Perimeter of the larger triangle will be 2 × perimeter of the smaller triangle. This becomes

2 × 11 = 22 units.

It can also be determined by adding the length of each side

3×2 + 3×2 + 5×2 = 6+6+10 = 22 units

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .