Question

the length of the base of an isosceles triangle is x. the length of a leg is 4x - 7. the perimeter of the triangle is 121. find x.

Explanation:

Step1: Set up the perimeter formula

The perimeter $P$ of an isosceles triangle with base length $x$ and leg - length $4x - 7$ is $P=x + 2(4x - 7)$. Since $P = 121$, we have the equation $x+2(4x - 7)=121$.

Step2: Expand the equation

Expand $2(4x - 7)$ to get $8x-14$. The equation becomes $x + 8x-14 = 121$.

Step3: Combine like - terms

Combine $x$ and $8x$ on the left - hand side: $9x-14 = 121$.

Step4: Isolate the variable term

Add 14 to both sides of the equation: $9x-14 + 14=121 + 14$, which simplifies to $9x=135$.

Step5: Solve for x

Divide both sides by 9: $\frac{9x}{9}=\frac{135}{9}$, so $x = 15$.

Answer:

$15$