Assume ΔABC∼ΔDEFΔ𝐴𝐵𝐶∼Δ𝐷𝐸𝐹. If the perimeter of ΔABCΔ𝐴𝐵𝐶 is 4848, the perimeter of ΔDEFΔ𝐷𝐸𝐹 is 7272, BC=3x𝐵𝐶=3𝑥, and EF=4x+2𝐸𝐹=4𝑥+2, find BC𝐵𝐶 and EF𝐸𝐹.BC=𝐵𝐶= EF=𝐸𝐹=
Question
Assume ΔABC∼ΔDEFΔ𝐴𝐵𝐶∼Δ𝐷𝐸𝐹. If the perimeter of ΔABCΔ𝐴𝐵𝐶 is 4848, the perimeter of ΔDEFΔ𝐷𝐸𝐹 is 7272, BC=3x𝐵𝐶=3𝑥, and EF=4x+2𝐸𝐹=4𝑥+2, find BC𝐵𝐶 and EF𝐸𝐹.BC=𝐵𝐶= EF=𝐸𝐹=
Solution
Given that ΔABC is similar to ΔDEF, the ratio of their perimeters is equal to the ratio of corresponding sides.
So, we have:
Perimeter of ΔABC / Perimeter of ΔDEF = BC / EF
Substituting the given values, we get:
48 / 72 = 3x / (4x + 2)
Solving this equation, we get:
2/3 = 3x / (4x + 2)
Cross multiplying, we get:
2*(4x + 2) = 3*3x
8x + 4 = 9x
Solving for x, we get:
x = 4
Substituting x = 4 in BC = 3x, we get BC = 3*4 = 12
Substituting x = 4 in EF = 4x + 2, we get EF = 4*4 + 2 = 18
So, BC = 12 and EF = 18.
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