Let's denote the base of the triangular field as \(b\) and the height as \(h\). The formula for the area (\(A\)) of a triangle is \(A = \frac{1}{2} \times \text{base} \times \text{height}\).
Given that the cost of cutting grass is Rs. 45 per 100 m² and the total cost is Rs. 900, we can write the equation:
\[ \frac{1}{2} \times b \times h \times \left(\frac{45}{100}\right) = 900 \]
Solving for \(b \times h\):
\[ b \times h = \frac{900 \times 2 \times 100}{45} \]
Now, it's mentioned that twice the base is 5 times the height:
\[ 2b = 5h \]
We can use this information to express \(b\) in terms of \(h\) and then substitute it into the previous equation to solve for \(h\). The answer would be the height of the triangular field.
Answers & Comments
Answer:
Let's denote the base of the triangular field as \(b\) and the height as \(h\). The formula for the area (\(A\)) of a triangle is \(A = \frac{1}{2} \times \text{base} \times \text{height}\).
Given that the cost of cutting grass is Rs. 45 per 100 m² and the total cost is Rs. 900, we can write the equation:
\[ \frac{1}{2} \times b \times h \times \left(\frac{45}{100}\right) = 900 \]
Solving for \(b \times h\):
\[ b \times h = \frac{900 \times 2 \times 100}{45} \]
Now, it's mentioned that twice the base is 5 times the height:
\[ 2b = 5h \]
We can use this information to express \(b\) in terms of \(h\) and then substitute it into the previous equation to solve for \(h\). The answer would be the height of the triangular field.