Question

# If triangle DEF is an isosceles triangle, angle d is the vertex angle, DE = 4x-7, EF = 3x+2 and DF = 6x- 15, find the value of x and the measure of each side

Answer

The value of x is 4, and the lengths of DE, DF, and EF are 9, 9, and 14, respectively. Step-by-step explanation: As the angle at vertex D, DE and DF have the same length. Therefore, we can set equation 4x - 7 = 6x - 15, and simplify it to 2x = 8, which gives us the value of x as 4. Then, we can calculate the lengths: DE = 4x - 7 = 4(4) - 7 = 16 - 7 = 9, DF = 9, and EF = 3(4) + 2 = 12 + 2 = 14.