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 given
s = 2lw + 2wh + 2lh; s = 76, l = 2, w = 5

h = \square

Explanation:

Step1: Substitute known values into formula

Substitute \( S = 76 \), \( L = 2 \), \( W = 5 \) into \( S = 2LW + 2WH + 2LH \):
\( 76 = 2\times2\times5 + 2\times5\times H + 2\times2\times H \)

Step2: Simplify the equation

Calculate \( 2\times2\times5 = 20 \), and simplify the terms with \( H \):
\( 76 = 20 + 10H + 4H \)
Combine like terms: \( 76 = 20 + 14H \)

Step3: Solve for H

Subtract 20 from both sides:
\( 76 - 20 = 14H \)
\( 56 = 14H \)
Divide both sides by 14:
\( H = \frac{56}{14} = 4 \)

Answer:

\( 4 \)