Question

1. the ratios of the measures of the sides of a triangle is 2:10:7. find the length of each side if the perimeter of the triangle is 228 meters.

short side=
medium side=
long side=

Explanation:

Step1: Find the sum of the ratio parts

The ratio of the sides is \(2:10:7\). The sum of the ratio parts is \(2 + 10+7=19\).

Step2: Find the value of one - part

The perimeter of the triangle is \(228\) meters. Let the length of each part be \(x\). Then \(19x = 228\), so \(x=\frac{228}{19}=12\).

Step3: Calculate the length of each side

• Short side: The ratio of the short side is \(2\). So the length of the short side is \(2x\). Substitute \(x = 12\), we get \(2\times12 = 24\) meters.
• Medium side: The ratio of the medium side is \(10\). So the length of the medium side is \(10x\). Substitute \(x = 12\), we get \(10\times12=120\) meters.
• Long side: The ratio of the long side is \(7\). So the length of the long side is \(7x\). Substitute \(x = 12\), we get \(7\times12 = 84\) meters.

Answer:

Short side \(=24\) meters, Medium side \(=120\) meters, Long side \(=84\) meters.