The lengths of the sides of a triangle are in the extended ratio 3 colon 10 colon 12. The perimeter is 400 cm. What is the length of the longest side in centimeters?
(1 point)
Responses
16 cm
16 cm
192 cm
192 cm
160 cm
160 cm
48 cm
To solve this problem, we can first find the common ratio by adding up the ratios: 3 + 10 + 12 = 25.
Next, we can find the scale factor by dividing the total perimeter by the common ratio: 400 cm ÷ 25 = 16 cm.
Finally, we can find the length of the longest side by multiplying the scale factor by the extended ratio of the longest side: 16 cm × 12 = 192 cm.
Therefore, the length of the longest side is 192 cm.
The correct answer is: 192 cm