A triangle is enlarged by a factor of 3. The perimeter of the new triangle is 36 feet. What could be the lengths of the sides of the original triangle?
A. 3 feet, 4 feet, and 5 feet
B. 1.5 feet, 1.25 foot, and 1.25 foot
C. 2 feet, 0.5 feet, and 1.8 feet
D. 4 feet, 4 feet, and 3 feet
pick the set with perimeter=12 since 12*3=36
To solve this problem, we need to understand how the sides of a triangle change when it is enlarged by a factor of 3.
When a triangle is enlarged, each side is multiplied by the factor of enlargement. In this case, the factor of enlargement is 3. So, if a side of the original triangle is x, the corresponding side of the enlarged triangle would be 3x.
Now, let's look at the possible lengths of the sides of the original triangle and see if they satisfy the given conditions.
A. 3 feet, 4 feet, and 5 feet
Using the enlargement factor of 3:
Enlarged triangle: 9 feet, 12 feet, and 15 feet
The perimeter of the enlarged triangle is 9 + 12 + 15 = 36 feet. Therefore, option A could be the answer.
B. 1.5 feet, 1.25 foot, and 1.25 foot
Using the enlargement factor of 3:
Enlarged triangle: 4.5 feet, 3.75 feet, and 3.75 feet
The perimeter of the enlarged triangle is 4.5 + 3.75 + 3.75 = 12 feet. Therefore, option B is incorrect.
C. 2 feet, 0.5 feet, and 1.8 feet
Using the enlargement factor of 3:
Enlarged triangle: 6 feet, 1.5 feet, and 5.4 feet
The perimeter of the enlarged triangle is 6 + 1.5 + 5.4 = 12.9 feet. Therefore, option C is incorrect.
D. 4 feet, 4 feet, and 3 feet
Using the enlargement factor of 3:
Enlarged triangle: 12 feet, 12 feet, and 9 feet
The perimeter of the enlarged triangle is 12 + 12 + 9 = 33 feet. Therefore, option D is incorrect.
From the analysis above, option A (3 feet, 4 feet, and 5 feet) is the only option that satisfies the given conditions. Therefore, the lengths of the sides of the original triangle could be 3 feet, 4 feet, and 5 feet.