Question

the length of the base of an isosceles triangle is x. the length of a leg is 3x - 2. the perimeter of the triangle is 73. find x

Explanation:

Step1: Write the perimeter formula

In an isosceles triangle, two sides (legs) are equal. The perimeter \(P\) of a triangle is the sum of all its sides. So \(P=x + 2(3x - 2)\).

Step2: Substitute the perimeter value

Since \(P = 73\), we have the equation \(x+2(3x - 2)=73\).
Expand the left - hand side: \(x + 6x-4=73\).

Step3: Combine like terms

Combine \(x\) and \(6x\): \(7x-4 = 73\).

Step4: Solve for \(x\)

Add \(4\) to both sides: \(7x=73 + 4\), so \(7x=77\).
Divide both sides by \(7\): \(x=\frac{77}{7}\).

Answer:

\(x = 11\)