Question

rp # 9 2. the ratio of the measures of the sides of a triangle is 9:7:3. if the perimeter of the triangle is 266 inches, find the length of the shortest side.

Explanation:

Step1: Set up the equation for the perimeter

Let the sides of the triangle be \(9x\), \(7x\), and \(3x\) (where \(x\) is a common multiplier). The perimeter \(P\) of a triangle is the sum of its sides. So, \(P=9x + 7x+3x\). Given \(P = 266\) inches. Then \(9x+7x + 3x=266\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(9x+7x + 3x=(9 + 7+3)x=19x\). So, the equation becomes \(19x=266\).

Step3: Solve for \(x\)

Divide both sides of the equation \(19x = 266\) by \(19\): \(x=\frac{266}{19}=14\).

Step4: Find the length of the shortest side

The shortest side is \(3x\). Substitute \(x = 14\) into \(3x\). So, \(3x=3\times14 = 42\) inches.

Answer:

The length of the shortest side is \(42\) inches.