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?

2 Answers
Aug 5, 2016

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

Aug 5, 2016

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

Tony BTony B