Question

I am really confused, can anyone help?

Answer 1

a = 24

b = 10

c = 26

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Step-by-step explanation:

We're given a list of possible b values and they are:

4, 5, 8, 10, 12, 24

Let's make a table to show what each value of 'a' would be based on those b values above.

`\begin{array}c \cline{1-2}b & a\\\cline{1-2}4 & 12\\\cline{1-2}5 & 14\\\cline{1-2}8 & 20\\\cline{1-2}10 & 24\\\cline{1-2}12 & 28\\\cline{1-2}24 & 52\\\cline{1-2}\end{array}`

Example calculation: If b = 4, then a = 2b+4 = 2*4+4 = 12 (first row)

I recommend using spreadsheet software to quickly compute these values. Also, a spreadsheet is useful to organize the data into a table.

Next we'll add a third column c.

This column will be computed using the formula
`c = √(a^2+b^2)` which is based from the pythagorean theorem
`a^2+b^2 = c^2`

So,

`\begin{array} \cline{1-3} & & \\b & a & c = √(a^2+b^2)\\\cline{1-3}4 & 12 & 12.6491\\\cline{1-3}5 & 14 & 14.8661\\\cline{1-3}8 & 20 & 21.5407\\\cline{1-3}10 & 24 & 26\\\cline{1-3}12 & 28 & 30.4631\\\cline{1-3}24 & 52 & 57.2713\\\cline{1-3}\end{array}`

Each decimal value mentioned is approximate. The only time c is an integer is when a = 24 and b = 10.

So that's how I got a = 24, b = 10, c = 26 as the final answer.