Question

In the following exercise a formula is given, along with the values of all but one of the variables in the formula. Find the value of the variable that is not givenS=2LW+2WH+2LH; S=52, L=2, W=3

Answer 1

H = 4

Step-by-step explanation

To identify which variable is missing, we can replace the variables we know the value by their value in the equation:

`S=2LW+2WH+2LH`

Replace S by 52, L by 2 and W by 3:

`52=2\cdot2\cdot3+2\cdot3\cdot H+2\cdot2\cdot H`

And solve the multiplications you can solve

`52=12+6H+4H`

We can see that the missing variable is H. To find its value, first we have to add like terms: this is to add the coefficients - the numbers that are multiplying the variable - of H:

`\begin{gathered} 52=12+(6+4)H \\ 52=12+10H \end{gathered}`

Now we have to substract 12 on both sides of the equation. This will leave us with only one term on the right side:

`\begin{gathered} 52-12=12-12+10H \\ 40=10H \end{gathered}`

Now that we have only one term where the variable is, we can divide both sides by 10, so the coefficient is cancelled and we'll get just the variable on the right side:

`\begin{gathered} (40)/(10)=(10H)/(10) \\ 4=H \end{gathered}`

The value of the variable is 4.