Question : The length of the base of an isosceles triangle is $2x-2y+4z$ and its perimeter is $4x-2y+6z$. Then the length of each of the equal sides is:
Option 1: $x+y$
Option 2: $x+y+z$
Option 3: $2(x+y)$
Option 4: $x+z$
Correct Answer: $x+z$
Solution :
Length of the base of an isosceles triangle = $2x - 2y + 4z$
Perimeter = $4x - 2y + 6z$
Let $l$ be the length of each of the equal sides.
Perimeter = 2(length of each of the equal sides) + length of the base of an isosceles triangle
⇒ $4x - 2y + 6z = 2l + 2x - 2y + 4z$
⇒ $2l = 4x - 2y + 6z - (2x - 2y + 4z)$
⇒ $2l = 2x + 2z$
⇒ $l=x+z$
So, the length of each of the equal sides = $x + z$
Hence, the correct answer is $x + z$.
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