perimetere of a rectangle is 155 inches it is 54 inches longer than the perimete of a triangle wat is the perimeter of the triangle

1. Break Down the Problem

We know that the perimeter of a rectangle is 155 inches and that it is 54 inches longer than the perimeter of a triangle. We need to find the perimeter of the triangle.

2. Relevant Concepts

The relationship between the perimeters can be expressed mathematically as: $P_{rectangle} = P_{triangle} + 54$ Where:

• $P_{rectangle}$ = perimeter of the rectangle
• $P_{triangle}$ = perimeter of the triangle

3. Analysis and Detail

Substituting the known value of the rectangle's perimeter: $155 = P_{triangle} + 54$ To find $P_{triangle}$, we rearrange the equation: $P_{triangle} = 155 - 54$ Now, we perform the calculation: $P_{triangle} = 101$

4. Verify and Summarize

Re-checking the calculation:

• Start with the equation: $155 = P_{triangle} + 54$
• Subtract 54 from 155 yields 101, which confirms our calculation.

Final Answer

The perimeter of the triangle is $101$ inches.