the lengths of the sides of a triangle are in the extended ratio 3:10:12. The perimeter is 400 cm. what is the length of the longest side in centimeters
To find the length of the longest side, we need to determine the value of the extended ratio.
The extended ratio in this case is 3:10:12, which means that the length of the sides can be represented as 3x, 10x, and 12x, where x is a common factor.
The sum of the lengths of the sides of a triangle is the perimeter.
Therefore, we have the equation:
3x + 10x + 12x = 400
Combining like terms, we get:
25x = 400
To isolate x, we divide both sides of the equation by 25:
x = 400/25
x = 16
Now we can find the length of the longest side:
12x = 12 * 16 = 192 cm
Therefore, the length of the longest side is 192 centimeters.