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Sagot :

Answer:  60 units

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Explanation:

The similar red marks on the angles tell us those angles are congruent. So they are the same measure.

The sides opposite those congruent angles are the same length. This means AC = BC. This triangle is isosceles.

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Solve for x

AC = BC

5x-8 = 2x+7 .... substitution

5x-8-2x = 7 ... subtract 2x from both sides

5x-2x = 7+8 ..... add 8 to both sides

3x = 15

x = 15/3 ... divide both sides by 3

x = 5

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Use that x value to compute each side length

AB = 3x+11 = 3*5+11 = 15+11 = 26

BC = 2x+7 = 2*5+7 = 10+7 = 17

CA = 5x-8 = 5*5-8 = 25-8 = 17

Note how BC and CA are the same length (17 units). This helps confirm we have the right x value.

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The last step is to add up all the side lengths to get the perimeter

perimeter of triangle = sum of all the sides

perimeter of triangle = side1 + side2 + side3

perimeter of triangle ABC = AB + BC + CA

perimeter of triangle ABC = 26 + 17 + 17

perimeter of triangle ABC = 60 units

jcherry99

Answer:

Step-by-step explanation:

Remark

The sides opposite the 2 base angles are equal. That gives you x. Then all you have to do is substitute in the 3 binomials.

Equation

5x - 8 = 2x + 7                 Add 8 to both sides

Solution

5x - 8 + 8 = 2x + 7 + 8   Combine

5x = 2x + 15                   Subtract 2x from both sides

5x-2x = 2x-2x + 15        Combine

3x = 15                           Divide by 3

x = 5

Side length

5x - 8 = 5*5 - 8 = 25 - 8

5x - 8 = 17

3x + 11 = 3*5 + 11 = 15 + 11 = 26

Perimeter

17

17

26    Add

Perimeter = 60

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