Question

In ΔABC, AB = 4x + 2, BC = 5x - 3, and AC = 2x + 4. The perimeter of the triangle is 36 units. Which angle in the triangle has the largest measure?

Answer 1

Answer: Angle C

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Step-by-step explanation:

Add up the three sides. Set the sum equal to the perimeter 36 so we can solve for x.

AB+BC+AC = perimeter

(4x+2)+(5x-3)+(2x+4) = 36

11x+3 = 36

11x = 36-3

11x = 33

x = 33/11

x = 3

Then use this x value to determine each side length.

• AB = 4x+2 = 4*3+2 = 14
• BC = 5x-3 = 5*3-3 = 12
• AC = 2x+4 = 2*3+4 = 10

The sides are

• AB = 14
• BC = 12
• AC = 10

As a check so far: 14+12+10 = 36 which helps confirm we have the correct x value, and correct side lengths.

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Rule: The largest angle is always opposite the longest side of a triangle.

We found that AB = 14 was the longest side. The opposite angle is C, which means this angle is the largest angle.

This is why angle C is the final answer.