Question

Given the formula \[V = LWH\], how do you solve for H in terms of V, W and L?

Answer 1

Hint: We need to find the value of ‘H’ in \[V = LWH\]. It’s a simple problem. We can solve this by dividing the whole equation by ‘LW’. We can also find the value of each term in terms of the remaining value that is ‘L’ in terms of V, H and W and so on. We use the transposition method in this problem. Here V, L, W and H are variables.

Complete step-by-step answer:
Given, \[V = LWH\]. That is we have V in terms of L, W and H.
We divide the above equation with ‘LW’ we get,
\[ \Rightarrow \dfrac{V}{{LW}} = \dfrac{{LWH}}{{LW}}\]
Cancelling terms we have,
\[ \Rightarrow \dfrac{V}{{LW}} = H\]
Rearranging the equation we have:
\[ \Rightarrow H = \dfrac{V}{{LW}}\]
Thus we have H in terms of V, W and L.
So, the correct answer is “ $ H = \dfrac{V}{{LW}} $ ”.

Note: Suppose if they ask us to find L in terms of H, V and W we need to divide the whole equation with WH then we have
 \[ \Rightarrow \dfrac{V}{{WH}} = \dfrac{{LWH}}{{WH}}\]
Cancelling the terms and rearranging the equation we have,
\[ \Rightarrow L = \dfrac{V}{{WH}}\]. Thus we have L in terms of H, V and W.
If they ask us to find W in terms of H, V and L we need to divide the whole equation with LH then we have
\[ \Rightarrow \dfrac{V}{{LH}} = \dfrac{{LWH}}{{LH}}\]
Cancelling the terms and rearranging the equation we have,
\[ \Rightarrow W = \dfrac{V}{{LH}}\]. Thus we have W in terms of H, V and L.
If they give the values of three variables we can find the other using above formulas.