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The lengths of the sides of ABCare consecutive integers. It ΔABC has perimeter as an equilateral triangle triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?
- a)8
- b)10
- c)4
- d)6
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The lengths of the sides of ABCare consecutive integers. It ΔABC...
Let the sides of ΔABC be n, n + 1, n + 2
⇒ Perimeter = n + n + 1 + n + 2
⇒ (9 + 9 + 9) = 3n + 3
⇒ 27 = 3n + 3
⇒ 3n = 24
⇒ n = 8 cm
Thus, the shortest side is 8 cm
⇒ Perimeter = n + n + 1 + n + 2
⇒ (9 + 9 + 9) = 3n + 3
⇒ 27 = 3n + 3
⇒ 3n = 24
⇒ n = 8 cm
Thus, the shortest side is 8 cm
Most Upvoted Answer
The lengths of the sides of ABCare consecutive integers. It ΔABC...
Given Information
- The lengths of the sides of ΔABC are consecutive integers.
- The perimeter of ΔABC is equal to the perimeter of an equilateral triangle with a side length of 9 cm.
Solution
To find the lengths of the sides of ΔABC, we first need to calculate the perimeter of the equilateral triangle with a side length of 9 cm. An equilateral triangle has all sides of equal length.
Perimeter of an equilateral triangle = 3 * side length
Perimeter of equilateral triangle = 3 * 9 cm = 27 cm
Since the perimeter of ΔABC is also 27 cm, the lengths of the sides of ΔABC are consecutive integers. Let's assume the lengths of the sides are x, x+1, and x+2 (consecutive integers).
According to the given information, x + x+1 + x+2 = 27
3x + 3 = 27
3x = 24
x = 8
Therefore, the lengths of the sides of ΔABC are 8 cm, 9 cm, and 10 cm. The shortest side of ΔABC is 8 cm, which corresponds to option 'A'.
- The lengths of the sides of ΔABC are consecutive integers.
- The perimeter of ΔABC is equal to the perimeter of an equilateral triangle with a side length of 9 cm.
Solution
To find the lengths of the sides of ΔABC, we first need to calculate the perimeter of the equilateral triangle with a side length of 9 cm. An equilateral triangle has all sides of equal length.
Perimeter of an equilateral triangle = 3 * side length
Perimeter of equilateral triangle = 3 * 9 cm = 27 cm
Since the perimeter of ΔABC is also 27 cm, the lengths of the sides of ΔABC are consecutive integers. Let's assume the lengths of the sides are x, x+1, and x+2 (consecutive integers).
According to the given information, x + x+1 + x+2 = 27
3x + 3 = 27
3x = 24
x = 8
Therefore, the lengths of the sides of ΔABC are 8 cm, 9 cm, and 10 cm. The shortest side of ΔABC is 8 cm, which corresponds to option 'A'.
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