Question 66019
QUESTION:

A rectangle is 10cm longer than it is wide. A line segment cute the area enclosed into two pieces, one of which is a square. The area of the rectangle os 118cm^2 more than the area of the square. What is the width of the rectangle?

ANSWER:


Given that length of a rectangle is 10cm longer than it is width,


So let's take  width = x cm  ( because length is given in terms of width.)


Then we have length = (x+10) cm


Then area of rectangle is = length * width



==> A = x ( x + 10 )


==>   = x^2 + 10x


Next it is given that area of rectangle is  118 more that of square.


Here we can take square with side "x"


So area of square = x*x = x^2

that is,

area of rectangle = area of square + 118


==>  x^2 + 10 x = x^2 + 118 


Subtract x^2 from both sides,


==> x^2 + 10 x - x^2 = x^2 + 118 -x^2


==> 10x = 118


Divide both sides by 10



==> 10x/10 = 118/10



==> x = 11.8



That is width of the rectangle is 11.8 cm




Hope you understood.



Regards.

praseena.