Question

10)The area of a rectangular field gets reduced by 80 square units if its length is reduced by 5 units and the breadth is increased by 2 units.If we increase the length by 10 units and decrease the breadth by 5 units, the area is increased by 50 sq units.

i) Find the length and breadth of the rectangular field.

ii) If one tree needs one sq unit, in which rectangular field more number planted. trees can be planted.​

Answer 1

Answer:

70

Step-by-step explanation:

Let the length and breadth of the rectangle be a,b units respectively.

Then the area will be ab square units.

Now if the length of the rectangle is reduced by 5 units and breadth is increased by 2 units then new length and breadth will be (a−5) units and (b+2) units.

Then new area will be (a−5)(b+2).

Then according to the problem,

(a−5)(b+2)−ab=−80

or, 2a−5b=−70...(1).

Now if length of the rectangle is increased by 10 units and breadth is decreased by 5 units then new length and breadth will be (a+10) units and (b−5) units.

Then new area will be (a+10)(b−5).

Then according to the problem,

(a+10)(b−5)−ab=50

or, 10b−5a=100

or, 2b−a=20

or, 4b−2a=40...(2).

Now adding (1) and (2) we get

−b=−30

or, b=30.

Putting the value of b in (1) we get, a=40.

Now a + b=40+30=70.