Question

the length of the base of an isosceles triangle is x. the length of a leg is 3x - 3. the perimeter of the triangle is 64. find x.

Explanation:

Step1: Write the perimeter formula for isosceles triangle

An isosceles triangle has two equal legs. The perimeter $P$ of an isosceles triangle is $P = \text{base}+ 2\times\text{leg}$. Given base $=x$, leg $=3x - 3$ and $P = 64$. So, $x+2(3x - 3)=64$.

Step2: Expand the equation

Using the distributive property $a(b + c)=ab+ac$, we expand $2(3x - 3)$ to get $6x-6$. The equation becomes $x + 6x-6=64$.

Step3: Combine like - terms

Combining the $x$ terms on the left - hand side, we have $(1 + 6)x-6=64$, which simplifies to $7x-6=64$.

Step4: Isolate the variable term

Add 6 to both sides of the equation: $7x-6 + 6=64 + 6$. This gives $7x=70$.

Step5: Solve for $x$

Divide both sides of the equation by 7: $\frac{7x}{7}=\frac{70}{7}$. So, $x = 10$.

Answer:

$10$