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
Answer:
The Answer is (A)
Step-by-step explanation:
A sample of each symbol (point, line, or area), and a short description of what the symbol means
Merry Christmas and a happy new year
Answer:
6.30
Step-by-step explanation:
Ivanka’s ribbon = 4.5 inches long
Michal’s ribbon is 3 1/2 times ivanka’s
Therefore,
Michal’s = 3 1/2 x 4.5
= 7/5 x 4.5
= 31.5/5
= 6.3 = 6.30 to the nearest hundredth
Answer:
John added 1 +4 +4 to get 9 (12x12 = 144)
Step-by-step explanation:
12x12 actually equals 144
1 + 4 +4 = 9 so it appears John just added all the digits of 144 to get 9
