a rectangle with one side of length 4cm is inscribed in a circle of diameter 5cm find the area of the rectangle.
it is from the chapter circle of understanding ICSE Mathematics class 10 by M.L Aggarwal.
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Let figure out the situation.
Inside the circle there are four corners of the rectangle touching the circumference of the circle. lets name this corners A,B,C and D respectively.
Now AB is a length and BC is a width of the rectangle. If we consider ABC it is a right triangle and AC is hypotenuse.AC goes through the center of the circle forming a diameter.
AB = 4
AC = 5
Using Pythagoras law
`AC^2 = AB^2+BC^2`
`5^2 = 4^2+BC^2`
`BC = 3`
So the rectangle has its legs as 4 and 3.
Area of rectangle = AB*BC = 4*3 = 12
Area of rectangle is `12cm^2`
The answer is clear .
since the rectangle is inscribed in the circle, the diameter of the circle = the diagonal of the rectangle=5cm
now the diagonal of the rectangle is the hypotenuse and let x be the other side of the rectangle
Using pythagoras theorem,
(x)^2 + (4)^2 = (5)^2
hence, x = 3 cm
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