Question 167806
Since you are dealing with right triangles use the Pythagorean Theorem.

a^2+b^2=c^2


side a=height of rectangle=2x-1
side b=width of rectangle=3x-1
Hypotenuse=diagonal =sq rt 5


Plug in

(2x-1)^2+(3x-1)^2=5

Use the foil method to expand the expression.

4x^2-4x+1+9x^2-6x+1=5

Combine like terms to simplify


13x^2-10x+2=5

Subtract 5 from both sides


13x^2-10x-3=0

Factor

(13x+3)(x-1)=0


x=-13/3 or 1
x cannot be a negative number so the only answer is x=1

side a=height of rectangle=2x-1=2-1=1
side b=width of rectangle=3x-1=3-1=2

area of a rectangle is axb=2