A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is
- \(\frac{22}{9+4\sqrt3}\)
- \(\frac{66}{9+4\sqrt3}\)
- \(\frac{22}{4+9\sqrt3}\)
- \(\frac{66}{4+9\sqrt3}\)
The Correct Option is B
Solution and Explanation
The correct option is(B): \(\frac{66}{9+4\sqrt3}\)
4a + 3b = 22
Total area = A
\(A=(\frac{22-3b}{4})^2+\frac{\sqrt3}{4}b^2\)
\(4\sqrt3b=66-9b\)
\(b=\frac{66}{9+4\sqrt3}\)
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Concepts Used:
Distance between Two Points
The distance between any two points is the length or distance of the line segment joining the points. There is only one line that is passing through two points. So, the distance between two points can be obtained by detecting the length of this line segment joining these two points. The distance between two points using the given coordinates can be obtained by applying the distance formula.
