Question

use the diagram shown to the right to find the unknown lengths of sides. the perimeter of the triangle is 165 feet. the length of the side measuring (5x) ft is . (simplify your answer. type an integer or a decimal)

Explanation:

Step1: Set up the perimeter equation

The perimeter of a triangle is the sum of the lengths of its sides. Let the sides be \(5x\), \(6x - 40\), and \(3x+40\). So, \(P=(5x)+(6x - 40)+(3x + 40)\). Given \(P = 165\), we have \((5x)+(6x - 40)+(3x + 40)=165\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(5x+6x+3x-40 + 40=165\), which simplifies to \(14x=165\).

Step3: Solve for \(x\)

Divide both sides of the equation \(14x = 165\) by 14: \(x=\frac{165}{14}\).

Step4: Find the length of the side \(5x\)

Substitute \(x=\frac{165}{14}\) into \(5x\): \(5\times\frac{165}{14}=\frac{825}{14}=58.928571\approx59\) (rounded to the nearest whole number).

Answer:

\(59\) feet