23a2012 wrote:
Rectangle ABCD is inscribed in a circle with center X. If the area of the rectangle is eight times its width, and the distance from X to side AB is three, what is the approximate circumference of the circle?
5
10
30
45
75
Area of the rectangle = L * B
Given, Area is 8 times its width i.e A = 8 * B --> L= 8
Since rectangle is inscribed within the circle, the diagonal BD is the diameter(2r) of the circle.
Given that the distance between X and AB is 3. (Connect a line from X to AB. This is basically the radius of the circle if you extend till the circle. it bisects AB equally at E)
The distance between B and E is 4 .
So basically it forms a right triangle with two sides 3 & 4. Hence the hypotenuse (i.e radius) is 5 (Pythogorean theorem)
Circumference is 2*pi* r =2 *22/7 * 5 = 31.blah blah
Hence answer is 30 ( question asks for the approximate one)
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