Question

The length of a rectangle plus its width is 25 cm. The area is 156 square cm. What are the length and width of the rectangle?

Answer 1

Length`=13`
Width`=12`

Explanation:

Let Length of the rectangle be `x`
Let Width of the rectangle be `y`
so
`x+y=25`
Area `=xy=156`
or
`2xy=312`
`(x+y)^2=25^2=625`
or
`x^2+y^2+2xy=625`
or
`x^2+y^2+312=625`
or
`x^2+y^2=313`
Therefore
`(x-y)^2=x^2+y^2-2xy`
or
`(x-y)^2=313-312`
or
`(x-y)^2=1`
or
`x-y=sqrt1`
or
`x-y=1`
and we have been given
`x+y=25`
Adding up both the equations
we get
`x+x-y+y=25+1`
or
`2x+0=26`
or
`2x=26`
or
`x=26/2`
or
`x=13`-------------Ans `1`
By putting the value of `x=13` in the equation `x+y=25`
We get
`13+y=25`
or
`y=25-13`
or
`y=12`--------------Ans `2`

Answer 2

`w=+12 and +13`

Explanation:

Let length be `L`
Let width be `w`
Lat area be `a`

Then `L+w=25`

`=>L=25-w`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`a=156=Lw =w(25-w)`

`=>-w^2+25w-156=0`

Multiply everything by (-1)

`=>w^2-25w+156=0`

Not that `(-12)xx(-13)=+156`

And that `-12-13=-25`

`(w-12)(w-13)=0`

`w=+12 and +13`