Rectangle - sides 3

If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we increases the area of the original rectangle by 5 cm².

Calculate the length of the sides of the rectangle ABCD.

Result

a =  15 cm
b =  7 cm

Solution:

(a+5)*(b-2) = a*b - 5
(a-4)*(b+3) = a*b + 5

2a-5b = -5
3a-4b = 17

a = 15
b = 7

Calculated by our linear equations calculator.

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Rectangles - sides
   One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm². What are the dimensions of the original rectangle?
2. Rectangular field
   One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m² . Determine dimencions of the field.
3. Hop-garden
   The length of the rectangular hop garden Mr. Smith increased by 25% and its width by 30%. What is the percentage change in area of hop garden?
4. Lawns
   Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?
5. Equations - simple
   Solve system of linear equations: x-2y=6 3x+2y=4
6. Mushrooms
   Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
7. Hotel rooms
   In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were?
8. Equations
   Solve following system of equations: 6(x+7)+4(y-5)=12 2(x+y)-3(-2x+4y)=-44
9. The dormitory
   The dormitory accommodates 150 pupils in 42 rooms, some of which are triple and some are quadruple. Determine how many rooms are triple and how many quadruples.
10. Waiting room
    In the waiting room are people and flies. Together they have 15 heads and 50 legs (fly has 6 legs). How many people and flies are in the waiting room?
11. Linear system
    Solve this linear system (two linear equations with two unknowns): x+y =36 19x+22y=720
12. Trees
    Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples?
13. Theatro
    Theatrical performance was attended by 480 spectators. Women were in the audience 40 more than men and children 60 less than half of adult spectators. How many men, women and children attended a theater performance?
14. Two numbers
    We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
15. Three brothers
    The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
16. Pages of book
    Lenka calculated that if every day to read 16 pages of the book, read a book a day earlier than had read only 14 pages a day. How many pages has this book?
17. Donuts
    In the dining room at one table sit Thomas, Filip and Martin. Together they eat 36 donuts. How many donuts eaten everyone, when Filip ate twice as much as Thomas and Martin even half over Filip?