:sam is 12 years older than john. for the last four years, sam and john have been friends. five years ago, sam was 5 times as old as john. how old is sam now?

The present age of Sam is 20 years .

Step-by-step explanation:

Given as :

Let The age of John =  J years

Let The age of Sam = S years

∵ Sam is 12 years older than John

so,  The age of Sam = 12 + The age of John

i.e S = 12 + J            .....1

Again

Before 5 years ago

The age of Sam = 5 times age of John

So, (S - 5) = 5 × (J - 5)

Or, S - 5 = 5 J - 25

Or, 5 J - S = 25 - 5

Or, 5 J - S = 20                  .........2

Solving eq 1 and eq 2

[5 J - (12 + J)] = 20

Or, 5 J - 12 - J = 20

Or, 4 J = 20 + 12

Or, 4 J = 32

∴ J =

i.e J = 8 years

So, The age of John = J = 8 years

Put The value of J into eq 1

∵ S = 12 + J

So, S = 12 + 8

i.e S = 20 years

So, The present age of Sam = S = 20 years .

Hence, The present age of Sam is 20 years . Answer

Sam is 20 years old now.

Step-by-step explanation:

Given:

Sam is 12 years older than John.

For the last four years, Sam and John have been friends.

Five years ago, Sam was 5 times as old as John.

Now, to find the age of Sam now.

Let the age of Sam be

And the age of John be

As, Sam is 12 years older than John.

Thus, .....( 1 )

Now, to get the age:

According to question:

.....( 2 )

Now, substituting the value of equation (1) in equation (2) we get:

Getting the variables in one side and numbers on the other we get:

Dividing both sides by 4 we get:

The age of John = 8 years.

Now, putting the value of in equation (1) we get:

Age of Sam = 20 years.

Therefore, Sam is 20 years old now.

Step-by-step explanation:

1) ABCD is a trapezium. AB ║ CD

∠ADC + ∠DAB  = 180°  { Co interior angles}

110° + ∠DAB = 180

         ∠DAB = 180 -110

∠DAB = 70°

2) Sum of all angles of trapezium = 360°

∠A + ∠B + ∠DCB + ∠D = 360

70° + 50° + ∠DCB + 110° = 360

                 230 + ∠DCB = 360

                            ∠DCB = 360 - 230

∠DCB = 130°

3) For finding the height, use Pythagorean theorem

height² + base² = hypotenuse²

      height² + 6² = 10²

      height² + 36 =100

               height² = 100 - 36

              height² = 64

               height = √64

height = 8 m

4) a = AB = x m

  b = 9 m

h = height = 8 m

Area of trapezium = 120 m²

 = 120

x + 9 = 120/4

x + 9 = 30

    x = 30 - 9

x = 21 m

AB = 21m