The lengths of the sides of a triangle are in the extended ratio . 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 find the lengths of the sides of the triangle, we can assign variables to the lengths, such as x, 2x, and 3x.
The extended ratio tells us that the lengths are in the ratio 1:2:3.
So, the lengths of the sides can be represented as:
Side 1 = x cm
Side 2 = 2x cm
Side 3 = 3x cm
The perimeter of a triangle is the sum of the lengths of its sides.
So, we have the equation:
Perimeter = Side 1 + Side 2 + Side 3
400 cm = x cm + 2x cm + 3x cm
Simplifying the equation:
400 cm = 6x cm
x = 400 cm / 6 = 66.67 cm (approximately)
The length of the longest side is 3x, which is:
3 * 66.67 cm = 200 cm (approximately)
Therefore, the length of the longest side is approximately 200 cm.