Question

1. the perimeter of the triangle at right is 100 sq. cm. write an equation and solve for x.

Explanation:

Step1: Set up the perimeter - equation

The perimeter of a triangle is the sum of the lengths of its sides. So, $x+(x + 5)+(2x+1)=100$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $(x+x + 2x)+(5 + 1)=100$, which simplifies to $4x+6 = 100$.

Step3: Isolate the variable term

Subtract 6 from both sides of the equation: $4x+6-6=100 - 6$, resulting in $4x=94$.

Step4: Solve for x

Divide both sides of the equation by 4: $x=\frac{94}{4}=\frac{47}{2}=23.5$.

Answer:

$x = 23.5$