Mathematics
Grade9
Easy
Question
The areas of two similar triangles are 45 square cm and 80 square cm. The sum of their perimeters is 35 cm. Find the perimeter of each triangle.
- 10 cm and 25 cm
- 15 cm and 20 cm
- 14 cm and 21 cm
- 16 cm and 19 cm
Hint:
Find the corresponding side length and then find the perimeter
The correct answer is: 15 cm and 20 cm
Let the two triangles, 
and 
and let the scale factor of the two similar triangles
Then, 
a : b is the reduced for of the scale factor, 3:4 is then the reduced form of the comparison of the perimeters.
Reduce the fraction
Take square roots of both sides.
Let 3x = perimeter of
and 4x = perimeter of
Then 3x + 4x = 35 (The sum of the perimeters in 35 cm)
7x = 35
x = 5
So,
Perimeter = 3(5) = 15 cm
Perimeter = 4(5) = 20 cm
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