Question

in a painting competition of a school a child made a flag whose perimeter was 50cm. its area will decreased by 6 sq.cm, if length is decreased by 3 cm and breadth is increased by 2 cm. find the dimension of flag..

Answer 1

You will need to set up a system of equations using the information given in the problem as follows:

We are given thaT the perimeter of the flag is 50 cm thus (letting x = length and y=width)

2x+2y=50 eq(1)

Also, the area reduction can be described as (letting A=area)

(x-3)(y-2)=A-6 eq(2)

now we have two equations and 3 unknowns, thus we need 1 more equation to be able to solve the system. We can use the equation that describes the original area of the flag as..

xy=A eq(3)


You can now simultaneously solve the system using a variety of different methods.

Answer 2

eq(2) should be (x-3)(y+2)=A-6 ... sorry typo

Answer 3

could u plz slve it fr me...!!!

Answer 4

There are a lot of different ways to solve the system. Including matrices, elimination, substitution etc.. It just depends on where you are at in your class.. You should take a stab at it using whatever ways you have been taught up to this point.

Answer 5

elimination method

Answer 6

you need to set some equations up first. the other commentators did a pretty decent job.
I'd just start out by doing this:
\[50cm=l+w+l+w, or 50cm=2l+2w\]

Answer 7

astrochyme is doing pretty much the same thing I would tell you.

Answer 8

I would start by expanding equation 2 and seeing what would be easiest to eliminate out of the equations

Answer 9

k

Answer 10

you could multiply eq3 by -1 and then add it to eq 2 to get rif of the A

then you can start playing with that new equation and equation 1

Answer 11

if you do that then you get

(x-3)(y+2)-xy=-6

expanding yields

xy+2x-3y-6-xy=-6

2x-3y=0 eq 4

now you have

2x+2y=50 eq1

2x-3y=0 eq 4

multiply equation 4 by -1 and add to equation 1 and repate the steps like I did above and you will solve for y. The plug y into equation 4 and solve for x.