Question

48. The area of a grassy plot is 480 sq. m. If each side
had been 5 m longer, the area would have been
increased by 245 sq. m. Find the length of the fence
to surround it.
(a) 87 m
(b) 88 m
(c) 90 m
(d) None of these

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Answer 1

Solution:-

Given:-

Area of Grassy plot = 480 m²

To Find:-

Length of the Fence= ?

Find:-

Let the length of the Grassy plot be "x" and that of breadth be "y".

=) x * y = 480 -----------(1).

If the sides are 5m Longer. Then Area;

Area = ( x + 5) ( y+5)

A.T.Q.

Area of 5m longer Grassy plot - Area of Grassy plot = 245

=) (x+5)(y+5) - xy = 245

=) xy + 5x + 5y + 25 - xy = 245

=) 5x + 5y = 245 - 25

=) 5( x+y) = 220

=) x + y = 44-----------(2)

Length of the Fence = Perimeter of the Grassy plot.

=) x + y = 44

Multiplying by 2 on both the sides. we get,

=) 2(x+y) = 2×44

=) Length of Fence = Perimeter of Grassy plot = 88 m.