1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
melamori03 [73]
3 years ago
10

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 incr

ease by 50 cm2. Find the length and the width of the original rectangle.
Mathematics
1 answer:
AVprozaik [17]3 years ago
6 0
X=length of the original rectangle.  (in cm)
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.
You might be interested in
Plz Help! NUmber 1 and 2! Brainlist for right answer!
Lerok [7]

Answer:

1 plain plain 2 ham chips

7 0
3 years ago
Read 2 more answers
The table below shows a correct representation that 15 pounds (lb) of sugar cost $3:
SIZIF [17.4K]

Answer: True

Step-by-step explanation: There are 15 pounds and 3 dollars. 15 over 3 is $1 for 5 pounds.

4 0
2 years ago
Please help..Thanks:)
finlep [7]
From top to bottom: 16, 5, 28. Please give me 'brainliest answer?
8 0
3 years ago
Read 2 more answers
PLEASE HELP ME!!!!!!!!!!!!!!!
Pachacha [2.7K]

Answer:

15 degrees

Step-by-step explanation:

angle a= (180-90)/2=90/2=45 degrees

angle QRP = 60

Angle b = 60-45=15 degrees

8 0
3 years ago
Find the quotient. (5x^4 - 3x^2 + 4) ÷ (x+1)​
lana [24]

Answer:x+12

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the sum of the first 14 terms of the sequence -11+(-18)+(-25)+(-32)...
    7·1 answer
  • HELP (I WILL GIVE 30 POINTS)
    13·2 answers
  • Beth sold half of her comic books and then bought 9 more. she now has 28. with how many did she begin? please show work. thanks
    5·2 answers
  • A bag contains 9 blue marbles and 3 red marbles. two marbles are drawn at random and at the same time. what is the probability o
    7·2 answers
  • Suppose AABC has coordinates A(2,3), B(5, 1), C(4.4), line m is the line with equation y = -5, and AABC is mapped to AA'B'C' by
    5·1 answer
  • Identifying Rigid Transformations
    8·2 answers
  • Solve for x. Pls and thank you.
    15·2 answers
  • Find PQ!!!!!!!!!!!!!!!!!!!!!!!
    12·1 answer
  • Prove that cos 2theta - cos 4theta + cos 6theta - cos 12theta = 4 sin 3theta sin 5theta cos 4theta
    10·2 answers
  • What is the scale factor from figure A to figure B?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!