Question

. The area of a rectangle decreases by 10 cm?
if the length is decreased by 5 cm and the
breadth is increased by 3 cm. If the length
is increased by 5 cm and the breadth is
increased by 2 cm, then the area increases
by 80 cm2. Find the perimeter of the rectangle.​

Answer 1

Answer:

302 cm

Step-by-step explanation:

So we will assume x as the length and y as the breadth of a rectangle.

When we find out the area of this rectangle it will be (xy)cm2.

Now if we decrease the length by 5, we are left with (x-5)cm and when we increase the breadth by 3 we have (y+3)cm.

Now if we subtract this area from the original area we should be left with 10 cm2.

xy-{(x-5)(y+3)}=10

xy-xy+5y-3x+15=10

5y-3x=-5   (1)

Now we will do the same thing with the other situation but this time the area is increasing by 80 so if we subtact the original area from the new area we will be left with 80cm2

New area:

(x+5)(y-2)

(x+5)(y-2)-xy=80

xy+5y-2x-10-xy=90

5y-2x=90         (2)

Now we just solve the two equations simultaneously:

-5+3x/5=90+2x/5

90+5=x

x=95

y=56

Perimeter=2(95+56)

                 =302 cm

I hope this helps you out!!