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The base of a triangular field is twice it's altitude. If the cost of leveling the field is at the rate of 10 per meter square is 4000. Find it's base and altitude.
Given :
The base of a triangular field is twice it's altitude.
The cost of leveling the field is ₹4000 at ₹10 per sq m.
To find :
We have to find the base and altitude.
Solution :
Let the altitude of the triangle be 'x'.
Then the base will be '2x'.
We know that the area of the triangle with base 'b' and height 'h' is,
$\frac{1}{2} \times b \times h$
Here, base $=2x$, height $= x$
So, Area of the triangle $=\frac{1}{2} \times 2x \times x = x^2$sq m.
The cost of leveling the field at ₹10 per sq m is ₹4000.
Area of the triangle $= \frac{4000}{10}$
Area of the triangle $= 400$sq m.
On comparing,
$x^2 = 400$sq m.
$x^2 = 20 \times 20$
$x = 20$m.
Altitude $= x = 20 $m.
Base $= 2x = 2(20) = 40$m.
Therefore, the base of the triangle is 40 and the altitude of the triangle is 20 m.
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