Alan

Like so:

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Let y be age of youngest.

y + (y + 1) + 3y = 21

5y + 1 = 21

5 y = 20

y = 4. Age of youngest

y + 1 = 5. Age of middle child

3y = 12. Age of oldest child.

Use v^2 = u^2 + 2as

v = 0 m/s. Final velocity

u = 80000/3600 m/s. Initial velocity

a = -7.5 m/s^2.  Acceleration (-ve sign indicating deceleration)

s is distance travelled in metres.

s = (80000/3600)^2/(2*7.5) m → 32.9 m

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We have:

 2(3x+c) + 7 = 3(2x+7) + c

6x + 2c + 7 = 6 x + 21 + c

2c + 7 = 21 + c

c = 14

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True.

This was answered here: https://web2.0calc.com/questions/factor-this-expression 

This graph should help (note: for x>=1 the two are the same):

This is the well known example of the 3-4-5 right angled triangle (each side is just twice 3, 4 and 5 respectively). So, yes, it must be a right angled triangle.

You can check using Pythagoras theorem: 6^2 + 8^2 → 36 + 64 → 100 and 10^2 → 100

i.e. The square on the hypotenuse is equal to the sum of the squares on the two adjacent sides (only true for right angled triangles).

Oops!  See CPhill's reply.

Part 1.  \(18\sqrt8\rightarrow 18\sqrt{2^2\times2}\rightarrow18\times2\sqrt2\rightarrow36\sqrt2\)

Part 2. \(8\sqrt{18}\rightarrow8\sqrt{3^2\times2}\rightarrow8\times3\sqrt2\rightarrow24\sqrt2\)

Part 3.  Now you have parts 1 and 2 you should be able to have a good go at this yourself.