Question

The area of garden is 420m square. If the width of the garden is 17 1/2 m What is the length of the garden?

Answer 1

let length be x metre and breadth be y metre

area of rectangular ground= area of rectangle

420=l b

420 =xy.................1

length is increased by 7m breadth is decreased by 5m

then area remain same

(X+7)(y-5)= 420

X(y-5)+7(y-5)=420

xy-5x+7y-35=420

420-5x+7y-35=420

-5x+7y-35=0

5x-7y+35=0

5x-7y= -35

-7y= -35-5x

y= -35-5x/-7

y= 35+5x/7

put y = 35+5x/7 in equation 1

420= X( 35+5x/7 )

420×7= 35x +5x2 .....2 means square

2940= 5x2 + 35x

5x2 +35x - 2940 = 0

devide whole equation by 5

X2 +35x -588=0

on solving

X= 28metre

y = 15 metre

Answer 2

l×b=420

l×17½=420

l=420/17½

l=420×2/17

l=840/17

l=49.41

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