3 questions please help

Question

I need help understanding these 

Tom is older than mike. the sum of their age is 75 and the difference of their age is 35, how old is tom

Answer: X(x+5)=84 How do i get this

x^2+5x-84=0

(x-7)(x+12)=0

tom is 7

 

One side of the rectangle is 5cm longer than the other. the area is 84cm^2. calculate the length width of the rectangle.

Answer: ?? i want the answer for this in steps with algerbraic terms PLEASE

 

A rectangle measures (x+3) by 5. write an expression fot the area

Answer: 4x+6=16 , how do i get this please explain in steps with algerbraic terms

after that how would i find the perimeter

Answer 1

1. Tom and Mike:

 

T+M = 75 and T-M =35 

On solving the above two equations we get, T = 55 and M = 20

 

2. Let's assume that one side of rectangle is x, then the other side will be x+5

 

Area of rectangle = x*(x+5) = 84

 

=> x^2+5x-84 = 0

=> (x+12)*(x-7) = 0

=> x = 7

 

so one of the side of the rectangle is 7 and other is 12. 

 

 

3. Sides of the rectangles are x+3 and 5

 

Formula for the area of rectangle = multiplication of sides

                                                = (x+3)*5

                                                = 5x+15