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The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4. If the perimeter is 52cm, then the length of the smallest side is
- a)9 cm
- b)10 cm
- c)11 cm
- d)12 cm
- e)none of these
Correct answer is option 'D'. Can you explain this answer?
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The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4. If the pe...
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The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4. If the pe...
Given:
The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4.
The perimeter of the triangle is 52 cm.
To find:
The length of the smallest side.
Solution:
Let's assume the sides of the triangle to be x, y, and z.
According to the given ratio, we have:
x:y:z = 1/2 : 1/3 : 1/4
Simplifying the ratio, we get:
x:y:z = 6:4:3
Let's assume the common ratio to be k.
So, x = 6k, y = 4k, and z = 3k.
The perimeter of the triangle is given by the sum of all three sides:
Perimeter = x + y + z
Substituting the values, we get:
52 = 6k + 4k + 3k
52 = 13k
Dividing both sides by 13, we get:
k = 4
Substituting the value of k back into the expressions for x, y, and z, we get:
x = 6(4) = 24
y = 4(4) = 16
z = 3(4) = 12
Therefore, the lengths of the sides of the triangle are 24 cm, 16 cm, and 12 cm.
The length of the smallest side is 12 cm.
Hence, the correct answer is option D) 12 cm.
The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4.
The perimeter of the triangle is 52 cm.
To find:
The length of the smallest side.
Solution:
Let's assume the sides of the triangle to be x, y, and z.
According to the given ratio, we have:
x:y:z = 1/2 : 1/3 : 1/4
Simplifying the ratio, we get:
x:y:z = 6:4:3
Let's assume the common ratio to be k.
So, x = 6k, y = 4k, and z = 3k.
The perimeter of the triangle is given by the sum of all three sides:
Perimeter = x + y + z
Substituting the values, we get:
52 = 6k + 4k + 3k
52 = 13k
Dividing both sides by 13, we get:
k = 4
Substituting the value of k back into the expressions for x, y, and z, we get:
x = 6(4) = 24
y = 4(4) = 16
z = 3(4) = 12
Therefore, the lengths of the sides of the triangle are 24 cm, 16 cm, and 12 cm.
The length of the smallest side is 12 cm.
Hence, the correct answer is option D) 12 cm.
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