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# ABC is a triangle. Angle ABC= angle BCA. The length of side AB is (3x-5) cm. The length of side AC is (19-x) cm. The length of side BC is 2x cm. Work out the perimeter of the triangle. Give your answer as a number of centimetres?

if angle abc=angle bca then we can assume the triangle is an isosceles. this means that side ab = side ac so 3x - 5 = 19 - x 3x + x = 19 + 5 4x = 24 x = 6 now that you have x, you can substitute this into all the sides and add them up to find the perimeter. ab + ac + bc = perimeter [3(6)-5] + [19-(6)] + [2(6)] = perimeter 13 + 15 + 12 = 40cm

Samantha Rajaratnam
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