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 B