Question

1. the longest side of a triangle is twice as long as the shortest side and the other side is 25 inches. if the perimeter of the triangle is 70 inches, what are the lengths of the longest and shortest sides?

Explanation:

Step1: Let the length of the shortest side be $x$.

Let the length of the shortest side be $x$ inches. Then the length of the longest side is $2x$ inches.

Step2: Set up the perimeter equation.

The perimeter of a triangle is the sum of the lengths of its sides. So $x + 2x+25 = 70$.

Step3: Combine like - terms.

Combining like - terms on the left - hand side gives $3x+25 = 70$.

Step4: Isolate the variable term.

Subtract 25 from both sides: $3x=70 - 25$, so $3x = 45$.

Step5: Solve for $x$.

Divide both sides by 3: $x=\frac{45}{3}=15$.

Step6: Find the length of the longest side.

The length of the longest side is $2x$. Substitute $x = 15$ into $2x$, we get $2\times15 = 30$.

Answer:

The length of the shortest side is 15 inches and the length of the longest side is 30 inches.