SOLUTION: Hi thanks a lot for offering to help this is great. The question gives me a rectangle with a height of 2x-1 and a width (base) of 3x-1. The question also says the length of a diag

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi thanks a lot for offering to help this is great. The question gives me a rectangle with a height of 2x-1 and a width (base) of 3x-1. The question also says the length of a diag      Log On


   

Question 167806This question is from textbook Mathematics for Edexcel IGCSE
: Hi thanks a lot for offering to help this is great.
The question gives me a rectangle with a height of 2x-1 and a width (base) of 3x-1. The question also says the length of a diagonal in the rectangle is the square root of 5. Calculate the area of the rectangle.
Thanks again This question is from textbook Mathematics for Edexcel IGCSE

Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
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