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 38. find x. x = □

Explanation:

Step1: Set up perimeter equation

An isosceles triangle has two equal legs. The perimeter $P$ of a triangle is the sum of the lengths of its sides. So, $P=x + 2(3x - 2)$. Given $P = 38$, we have the equation $x+2(3x - 2)=38$.

Step2: Expand the equation

Using the distributive property $a(b + c)=ab+ac$, we expand $2(3x - 2)$ to get $6x-4$. The equation becomes $x + 6x-4=38$.

Step3: Combine like - terms

Combining the $x$ terms on the left - hand side, $x+6x=7x$. So the equation is $7x-4 = 38$.

Step4: Add 4 to both sides

To isolate the term with $x$, we add 4 to both sides of the equation. $7x-4 + 4=38 + 4$, which simplifies to $7x=42$.

Step5: Solve for x

Divide both sides of the equation $7x = 42$ by 7. $\frac{7x}{7}=\frac{42}{7}$, so $x = 6$.

Answer:

$6$