The perimeter of a rectangle is 70 cm. If its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm2. Find the length and the width of the original rectangle.
Answers
y=width o f the original rectangle. (in cm)
Perimeter of a rectangle=sum of the all sides.
Perimeter of the original rectangle=x+x+y+y=2x+2y
Area of a rectangle=length x width
Area of the original rectangle=xy
x-5=length decreased by 5 cm
y+5=width increase by 5 cm.
We can suggest this system of equations:
2x+2y=70
(x-5)(y+5)=xy+50
We solve this system of equations by susbstitution method:
2x+2y=70 ⇒x+y=35 ⇒ y=35-x
(x-5)(35-x+5)=x(35-x)+50
(x-5)(40-x)=35x-x²+50
40x-x²-200+5x=35x-x²+50
40x-35x+5x=200+50
10x=250
x=250/10
x=25
y=35-x
y=35-25
y=10
Answer: the lenght and the width of the original rectangle is :
lenght=25 cm
width=10 cm.
The length of the rectangle is 25cm and the width of the rectangle is 45cm and this can be determine by forming the linear equations.
Given :
- Perimeter of a rectangle is 70 cm.
- Rectangle length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50
.
Let 'a' be the length of the rectangle and 'b' be the width of the rectangle. Than the perimrter of the rectangle will be:
a + b = 70 ---- (1)
Now, the area of the rectangle will be:
a = 25
Now, put the value of 'a' in equation (1).
b = 70 - 25 = 45
b = 45
Therefore, the length of the rectangle is 25cm and the width of the rectangle is 45cm.
For more information, refer the link given below:
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b. Sometimes
c. Never
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Beef:Pork = 3 : 1
Total ratio = 3 + 1 = 4
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Hope this explains it.
Answers
The power is a minus as the decimal point had to move right.
Hope that helps you!
A.
Translate into an equation. (30 + 45 + 35) ÷ 6 = m
B.
Use logical reasoning. Add together the number of minutes Ella babysits each week: 30 + 45 + 35 = 110. Multiply 110 by the number of weeks Ella continues this babysitting schedule.
C.
Draw a diagram. Draw 6 large squares. Add up the numbers 30, 45, and 35 to get 110. Write 110 in each square. Add up the numbers in the squares.
D.
Make a table.
Week 1 2 3 4 5 6
Total (minutes): 110 220 330 440 550
Answers
The letter A goes m=(30+45+35)/6, the question asked how many minutes Ella will babysit in six weeks. In a week Ella babysits for 110 minutes, instead of dividing it by 6 weeks (which is shown in the equation of letter A), you have to multiply by 6 weeks. It should go like this, m= (30+45+35) x 6.
B. a number greater than 4
C. a multiple of 3
D. an even number
Answers
(desired outcomes)/(total possible outcomes)
total possible is 8 since 8 total spaces
A. number les than 4, there are 3 numbers (1,2,3) so
3/8 os probability
B. number greater than 4, ther are 4 (5,6,7,8), so 4/8=1/2 is probability
C. multiplule of 3, there are 2 (3,6) so 2/8=1/4 is probability
D. even number, there are 4 (2,4,6,8) so 4/8=1/2 is probability
A. 3/8
B. 1/2
C. 1/4
D. 1/2