Questions on Algebra: Quadratic Equation answered by real tutors!

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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 againThis 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
Answer by KnightOwlTutor(291) 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