Here given, radius = 2 m
Diameter of the circle will be = 2 2 m = 4
4 will be the diagnal of the rectangular playground.
Now let, length be 4x m and width be 5x m.
According to Pythagorean theorem,
(4x)2 + (5x)2 = (4)2
= 16x2 + 25x2 = 16 41
=41x2 = 16 41
x2 = = 16
x = = = 4
Area will e = 4x 5x = 20x2 = 20 42 = 20 16 = 320m2
17.
Two numbers x, y are in G.P and their sum is 30. Also, the sum of their squares is 468. Find the numbers.
(Series)
Two numbers x, y are in G.P and their sum is 30. Also, the sum of their squares is 468. Find the numbers.
(Series)Let, one number is x and another one is y
According to question
x + y = 30 .......... (i)
And x2 + y2 = 468 ............(ii)
From equation (i), x + y = 30
⇒x=30-y........ (iii)
putting x = 30 - y in equation (ii)
x2 + y2 = 468
=(30 - y)2 + y2 = 468
= 900 - 60y + y2 + y2 = 468
=2y2 - 60y + 432 = 0
=y2 - 30y + 216 = 0
=y2 - 18y - 12y + 216 = 0
=y(y - 18) - 12(y - 18) = 0
=(y - 18)(y - 12) = 0
Here, y - 18 = 0
y = 18
Or, y - 12 = 0
y = 12
Putting y = 18 in equation (iii), we get
x = 30 - 18 = 12
x = 12
Putting y = 12 , in equation (iii) we get
x = 30 - 12 = 18
x = 18
(answer) (x, y) = (12, 18) Or, (18, 12).
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