MATH question plz help!!!?

Question

ok its a pretty easy math question but i still don't understand them there is two of them

1) the sides of a rectangle are in the ration 3:2. what is the length of each side if the perimeter of the rectangle is 55 cm.

and number 2 is

2) the sum of three consecutive integers is 90

a)find the 3 numbers by letting x represent the first integer.

b)find the three numbers by letting x represent the second integer.

plz help me and also try to explain how you got the answer

thank you

Answer 1

1)

Let 'l' be the length of the rectangle.

Let 'b' be the breadth of the rectangle.

l : b = 3 : 2, which can also be written as:

(l / b) = (3 / 2).

=> l = (3b / 2).

The perimeter of the rectangle is 2(l + b) = 55.

=> 2[(3b / 2) + b] = 55.

=> 2[(3b + 2b)/2] = 55.

=> (3b + 2b) = 55.

=> b = 55/5 = 11.

So, breadth = 11 cm.

=>  l = (3b / 2) as written above. So, l =  (33 / 2), => 16.5

So, length of the rectangle is 16.5 cm and breadth of the rectangle is 5 cm.

_____________________________________

2)

a)Let the first number be 'x'. Since the numbers are consecutive, they're (x), (x+1), (x+2) [ WRITTEN IN TERMS OF 'x', being the first number].....

So, (x) + (x+1) + (x+2) = 90, as the sum of the 3 consecutive numbers is 90.

=> 3x + 3 = 90.

=> 3x = 87.

=> x = 29.

Since 'x' = 29, (x + 1) = 30, (x + 2) = 31. The 3 numbers are 29, 30, 31.

_____________________________________

b)

Let the 2nd number of the 3 numbers be 'x'. So, the other two numbers are (x-1), (x+1).

SO, the 3 numbers are (x-1), (x), (x+1)[ WRITTEN IN TERMS OF 'x', being the second integer].....

The sum of 3 numbers is 90:

(x-1) + (x) + (x+1) = 90.

=> 3x = 90.

=> x = 30.

So, the second integer is 30. he other two integers are:

(x-1) = 29.

(x+1) = 31.

The 3 numbers (x-1), (x), (x+1) are 29, 30, 31....

Hope my answer was useful enough to clear your doubts.

Answer 2

part 1:

3:2 is the ratio = 3/2(fraction)=1.5

rectangle has 4 sides(4 unknowns represented with x)...2 sides being longer than the other 2 sides

so the 2 longer sides is represented by 3/2x

and the 2 shorter sides is represented by x

add all the x's up:

x+x+3/2x+3/2x=5x

solve for x

5x=55

x=55/5

x=11

plug in 11 for x.....3/2*11= 16.5

check your answer:

11+11+16.5+16.5= 55