Question

1. the length of the base of an isosceles triangle is 2x. the length of one leg is 4x - 20. the perimeter of the triangle is 40. what is the value of x?

Explanation:

Step1: Set up the perimeter formula

The perimeter of an isosceles triangle is the sum of the base and the two equal legs. So, \(P = 2x+(4x - 20)+(4x - 20)\).

Step2: Substitute the perimeter value

Since \(P = 40\), we have \(40=2x+(4x - 20)+(4x - 20)\).

Step3: Simplify the equation

First, combine like - terms: \(40=2x + 4x-20+4x - 20\), which simplifies to \(40=(2x + 4x+4x)-(20 + 20)\), or \(40 = 10x-40\).

Step4: Solve for \(x\)

Add \(40\) to both sides: \(40 + 40=10x-40 + 40\), so \(80 = 10x\). Then divide both sides by \(10\): \(x=\frac{80}{10}\).

Answer:

\(x = 8\)