Question

I’m not sure how to slove this problem it’s a equilateral triangle and I’m trying to find out what the side is equal to.

Answer 1

Answer as a fraction: AB = 127/13 (exact)

Answer in decimal form: AB = 9.76923 (approximate)

Sides AC and BC are the same length as AB.

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Work Shown:

AB = (3/2)x+4

AC = (1/5)x+9

These sides are equal to each other since all sides of an equilateral triangle are the same length.

AB = AC

(3/2)x+4 = (1/5)x+9

10*[ (3/2)x+4 ] = 10*[ (1/5)x+9 ] ... see note below

10*(3/2)x + 10*4 = 10*(1/5)x + 10*9

15x + 40 = 2x + 90

15x-2x = 90-40

13x = 50

x = 50/13

Note: I multiplied both sides by the LCD (lowest common denominator) 10 to clear out the fractions.

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Once we know what x is, we plug it into the expression for AB

AB = (3/2)x+4

AB = (3/2)*(50/13) + 4

AB = (3*50)/(2*13) + 4

AB = (3*2*25)/(2*13) + 4

AB = (3*25)/(13) + 4

AB = 75/13 + 4

AB = 75/13 + 52/13

AB = (75+52)/13

AB = 127/13 which is exact

AB = 9.76923 which is approximate

Because we have an equilateral triangle, AB = BC = AC.