Two similar triangles have perimeters in the ratio 3:5. The sides of the smaller triangle measure 3 cm, 5 cm, and 7 cm, respectively. What is the perimeter, in centimeters, of the larger triangle?Responses151518182020252536
Question
Two similar triangles have perimeters in the ratio 3:5. The sides of the smaller triangle measure 3 cm, 5 cm, and 7 cm, respectively. What is the perimeter, in centimeters, of the larger triangle?Responses151518182020252536
Solution
The problem states that the perimeters of the two similar triangles are in the ratio 3:5. This means that each side of the larger triangle is 5/3 times the length of the corresponding side of the smaller triangle.
The sides of the smaller triangle are 3 cm, 5 cm, and 7 cm. Therefore, the sides of the larger triangle are (5/3)*3 cm, (5/3)*5 cm, and (5/3)*7 cm, which simplifies to 5 cm, 25/3 cm, and 35/3 cm, respectively.
The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of the larger triangle is 5 cm + 25/3 cm + 35/3 cm = 60/3 cm = 20 cm.
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