Question

the length of the base of an isosceles triangle is x. the length of a leg is 2x - 3. the perimeter of the triangle is 44. find x. x =

Explanation:

Step1: Write the perimeter formula

The perimeter \( P\) of an isosceles triangle with base \(x\) and two equal legs (each of length \(2x - 3\)) is \(P=x+(2x - 3)+(2x - 3)\).

Step2: Simplify the equation

Combine like - terms: \(P=x + 2x-3+2x - 3=5x-6\).
Since \(P = 44\), we have the equation \(5x-6 = 44\).

Step3: Solve for \(x\)

Add \(6\) to both sides: \(5x-6 + 6=44 + 6\), so \(5x=50\).
Divide both sides by \(5\): \(x=\frac{50}{5}\).

Answer:

\(10\)