Question

the length of the base of an isosceles triangle is x. the length of a leg is 2x - 7. the perimeter of the triangle is 26. find x. x =

Explanation:

Step1: Write the perimeter formula

The perimeter \(P\) of an isosceles triangle is \(P=\text{base}+ 2\times\text{leg}\). Given base \(=x\), leg \(=2x - 7\), and \(P = 26\), we have \(x+2(2x - 7)=26\).

Step2: Expand the equation

Expand \(2(2x - 7)\) using the distributive property \(a(b + c)=ab+ac\). So \(2(2x-7)=4x-14\), and the equation becomes \(x + 4x-14=26\).

Step3: Combine like - terms

Combine \(x\) and \(4x\). \(x+4x=5x\), so the equation is \(5x-14 = 26\).

Step4: Isolate the variable term

Add 14 to both sides of the equation. \(5x-14 + 14=26+14\), which simplifies to \(5x=40\).

Step5: Solve for \(x\)

Divide both sides by 5. \(\frac{5x}{5}=\frac{40}{5}\).

Answer:

\(x = 8\)