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The base of a triangular wall is 7 times its height. If the cost of painting the wall at Rs. 350 per 100 sq m is Rs. 1225, then what is the base length?
- a)50 m
- b)70 m
- c)75 m
- d)100 m
Correct answer is option 'B'. Can you explain this answer?
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The base of a triangular wall is 7 times its height. If the cost of pa...
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The base of a triangular wall is 7 times its height. If the cost of pa...
To find the base length of a triangular wall, we need to use the given information about the ratio of the base to the height and the cost of painting the wall.
Let's assume the height of the triangular wall is 'h' meters.
According to the given information, the base of the triangular wall is 7 times its height. Therefore, the base length will be 7h meters.
To find the area of the triangular wall, we use the formula: Area = (1/2) * base * height
Substituting the values, we get: Area = (1/2) * (7h) * h = (7/2) * h^2
We are given that the cost of painting the wall is Rs. 350 per 100 sq m. So, the cost of painting the triangular wall will be:
Cost = (Area / 100) * 350
Substituting the value of the area, we get: Cost = [(7/2) * h^2 / 100] * 350
Given that the cost is Rs. 1225, we can write the equation as:
1225 = [(7/2) * h^2 / 100] * 350
Simplifying the equation, we get:
[(7/2) * h^2 / 100] * 350 = 1225
Cancelling out the common factors, we get:
(7/2) * h^2 = 35
Now, let's solve for h by dividing both sides by (7/2):
h^2 = 35 / (7/2) = (35 * 2) / 7 = 10
Taking the square root of both sides, we get:
h = √10
Therefore, the height of the triangular wall is √10 meters.
To find the base length, we multiply the height by 7:
base length = 7 * √10 = √(7^2 * 10) = √(49 * 10) = √490 = 7√10
So, the base length of the triangular wall is 7√10 meters, which is approximately 26.46 meters.
Therefore, the correct answer is option (B) 70 m.
Let's assume the height of the triangular wall is 'h' meters.
According to the given information, the base of the triangular wall is 7 times its height. Therefore, the base length will be 7h meters.
To find the area of the triangular wall, we use the formula: Area = (1/2) * base * height
Substituting the values, we get: Area = (1/2) * (7h) * h = (7/2) * h^2
We are given that the cost of painting the wall is Rs. 350 per 100 sq m. So, the cost of painting the triangular wall will be:
Cost = (Area / 100) * 350
Substituting the value of the area, we get: Cost = [(7/2) * h^2 / 100] * 350
Given that the cost is Rs. 1225, we can write the equation as:
1225 = [(7/2) * h^2 / 100] * 350
Simplifying the equation, we get:
[(7/2) * h^2 / 100] * 350 = 1225
Cancelling out the common factors, we get:
(7/2) * h^2 = 35
Now, let's solve for h by dividing both sides by (7/2):
h^2 = 35 / (7/2) = (35 * 2) / 7 = 10
Taking the square root of both sides, we get:
h = √10
Therefore, the height of the triangular wall is √10 meters.
To find the base length, we multiply the height by 7:
base length = 7 * √10 = √(7^2 * 10) = √(49 * 10) = √490 = 7√10
So, the base length of the triangular wall is 7√10 meters, which is approximately 26.46 meters.
Therefore, the correct answer is option (B) 70 m.
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The base of a triangular wall is 7 times its height. If the cost of painting the wall at Rs. 350 per 100 sq m is Rs. 1225, then what is the base length?a)50 mb)70 mc)75 md)100 mCorrect answer is option 'B'. Can you explain this answer?
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