Question

the lengths of the sides of a triangle are in the extended ratio 6 : 7 : 9. the perimeter of the triangle is 110 cm. what are the lengths of the sides?
the lengths of the sides of the triangle in cm are
(use a comma to separate answers as needed. )

Explanation:

Step1: Find the sum of the ratio parts

The ratio of the sides is \(6:7:9\). First, we calculate the sum of the ratio components. So, \(6 + 7+9=22\).

Step2: Determine the value of one part

The perimeter of the triangle is \(110\) cm. Since the sum of the ratio parts is \(22\), we find the value of one part by dividing the perimeter by the sum of the ratio parts. That is, \(\frac{110}{22} = 5\).

Step3: Calculate the length of each side

• For the first side with ratio \(6\): Multiply the value of one part by \(6\). So, \(6\times5 = 30\) cm.
• For the second side with ratio \(7\): Multiply the value of one part by \(7\). So, \(7\times5=35\) cm.
• For the third side with ratio \(9\): Multiply the value of one part by \(9\). So, \(9\times5 = 45\) cm.

Answer:

30, 35, 45