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If the area of a rectangle is 24 m2 and its perimeter is 20 m, the equation to find its length and breadth would be:
- a)x2 – 10x + 24 = 0
- b)x2 + 1 2x + 24 = 0
- c)x2 – 10x – 24 = 0
- d)x2 + 10x + 28 = 0
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the area of a rectangle is 24 m2and its perimeter is 20 m, the equa...
Perimeter = 2(l+b)=20
l+b=10
lxb=24
so correct option is A
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If the area of a rectangle is 24 m2and its perimeter is 20 m, the equa...
Let's assume the length of the rectangle is L and the breadth is B.
The formula for the area of a rectangle is A = L * B, and the formula for the perimeter is P = 2L + 2B.
Given that the area is 24 m² and the perimeter is 20 m, we can write the following equations:
24 = L * B (Equation 1)
20 = 2L + 2B (Equation 2)
To solve for L and B, we can rearrange Equation 1 to solve for L:
L = 24 / B
Substituting this value of L into Equation 2, we have:
20 = 2 * (24 / B) + 2B
Simplifying, we get:
20 = 48 / B + 2B
Multiplying through by B to eliminate the denominator, we have:
20B = 48 + 2B²
Rearranging, we get:
2B² + 20B - 48 = 0
Dividing through by 2, we have:
B² + 10B - 24 = 0
Factoring the quadratic equation, we get:
(B + 12)(B - 2) = 0
This gives us two possible values for B: B = -12 or B = 2. However, since we are dealing with measurements, we can discard the negative value.
Therefore, the breadth of the rectangle is B = 2.
Substituting this value back into Equation 1, we can solve for L:
24 = L * 2
Dividing through by 2, we have:
L = 12
Thus, the length of the rectangle is L = 12 meters and the breadth is B = 2 meters.
The formula for the area of a rectangle is A = L * B, and the formula for the perimeter is P = 2L + 2B.
Given that the area is 24 m² and the perimeter is 20 m, we can write the following equations:
24 = L * B (Equation 1)
20 = 2L + 2B (Equation 2)
To solve for L and B, we can rearrange Equation 1 to solve for L:
L = 24 / B
Substituting this value of L into Equation 2, we have:
20 = 2 * (24 / B) + 2B
Simplifying, we get:
20 = 48 / B + 2B
Multiplying through by B to eliminate the denominator, we have:
20B = 48 + 2B²
Rearranging, we get:
2B² + 20B - 48 = 0
Dividing through by 2, we have:
B² + 10B - 24 = 0
Factoring the quadratic equation, we get:
(B + 12)(B - 2) = 0
This gives us two possible values for B: B = -12 or B = 2. However, since we are dealing with measurements, we can discard the negative value.
Therefore, the breadth of the rectangle is B = 2.
Substituting this value back into Equation 1, we can solve for L:
24 = L * 2
Dividing through by 2, we have:
L = 12
Thus, the length of the rectangle is L = 12 meters and the breadth is B = 2 meters.
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If the area of a rectangle is 24 m2and its perimeter is 20 m, the equation to find its length and breadth would be:a)x2– 10x + 24 = 0b)x2+ 1 2x + 24 = 0c)x2– 10x – 24 = 0d)x2+ 10x + 28 = 0Correct answer is option 'A'. Can you explain this answer?
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