Question

the length of the base of an isosceles triangle is x. the length of a leg is 5x - 5. the perimeter of the triangle is 100. find x.
x =

Explanation:

Step1: Write the perimeter formula

In an isosceles triangle, two legs are equal. Perimeter \(P=\text{base}+ 2\times\text{leg}\). So \(100=x + 2(5x - 5)\).

Step2: Expand the equation

Expand \(2(5x - 5)\) using the distributive property \(a(b + c)=ab+ac\). We get \(100=x+10x - 10\).

Step3: Combine like - terms

Combine \(x\) and \(10x\). The equation becomes \(100 = 11x-10\).

Step4: Isolate the variable term

Add \(10\) to both sides of the equation: \(100 + 10=11x-10 + 10\), which simplifies to \(110 = 11x\).

Step5: Solve for \(x\)

Divide both sides by \(11\): \(x=\frac{110}{11}\).

Answer:

\(x = 10\)