What is the area of a rectangle with length #(2x+2)#, width #(x)# and a diagonal of 13?

1 Answer
Jan 1, 2016

The area of such rectangle is #60#.

Explanation:

Using the Pythagorean Theorem #a^2+b^2=c^2#, we substitute the expressions into the equation:

#x^2+(2x+2)^2=13^2#
#x^2+4x^2+8x+4=169#
#5x^2+8x-165=0#

Factor the equation:

#(5x^2-25x)+(33x-165)=0#
#5x(x-5)+33(x-5)=0#
#(5x+33)(x-5)=0#

The two solutions we find are #-33/5# and #5#. Since we cannot have a negative width, we immediately discard the negative solution, leaving us with #x=5#.

Now we simply solve for the area by substituting #x# with #5#, and we get our answer:

#2(5)+2=10+2=12#
#5*12=60#