Question

EFG is isosceles with F as the vertex angle. Given EF = 4x, FG = 3x + 2, and GE = 3x, find the value of x and the measurements of each side. A) x = 2, EF = 8, FG = 8, GE = 6 B) x = 4, EF = 16, FG = 14, GE = 12 C) x = 3, EF = 12, FG = 11, GE = 9 D) x = 5, EF = 20, FG = 17, GE = 15

Answer 1

An isosceles triangle is one where two sides are of equal length. In triangle EFG with F as the vertex angle, the two sides that are equal in length are EF and FG (since these connect to the vertex angle F). Therefore, since EF = 4x and FG = 3x + 2, it follows that 4x = 3x + 2 (because EF = FG).

Solving this equation will give the value of x. Subtracting 3x from both sides gives x = 2. Once we have x, we can use it to find the measurements of the sides:

• EF = 4x = 4*2 = 8
• FG = 3x + 2 = 3*2 + 2 = 8
• GE = 3x = 3*2 = 6

So, the value of x is 2, and the measurements of the sides EF, FG, and GE are 8, 8, and 6 respectively. Therefore, the answer is A) x = 2, EF = 8, FG = 8, GE = 6.

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