If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width
Solution:
Let the length of rectangle=x
Width of rectangle=x/10
Perimeter is 2(Length+Width)
= 2(x+x/10)
Area of Rectangle= Length* Width=x*x/10
As, Perimeter=2(Area)
So,2(x+x/10)=2(x*x/10)
Multiplying the equation with 10, we get,
2(10x+x)=2x²
Adding Like terms, 10x+x=11x
2(11x)=2x^2
22x=2x²
2x²-22x=0
2x(x-11)=0
By Zero Product property, either x=0
or, x-11=0
or, x=11
So, Width=x/10=11/10=1.1
Checking:
So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2
Area=Length*Width=11*1.1=12.1
Hence, Perimeter= 2 Area
As,24.2=2*12.1=24.2
So, Perimeter=2 Area
So, Answer:Length of Rectangle=11 units
Width of Rectangle=1.1 units
A= bh(1/2)
a=12(14)(1/2)
a= 168(1/2)
a= 84inches
Answer:
Yes
Step-by-step explanation:
To see if (2,0) works as a solution to the systems of equations, we plug in the values of x and y and simplify. If the results are equal, then (2,0) is a solution.
3x + y = 6:
- (2,0) is a solution to this equation.
3x - y = 6:
-
- (2,0) is a solution to this equation.
Therefore, the answer is yes, it does work as a solution.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
9/4<x≤4 or all real numbers
Step-by-step explanation:
I'm not sure what you are asking
