Answer: The value of q is exactly 7
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Step-by-step explanation:
L = 16 is the length
W = 3 is the width
H = q is the unknown height
S = 362 is the surface area
We'll use the formula
S = 2*(L*W+W*H+L*H)
which is the surface area formula for any rectangular block
So plug in the given info and solve for q
S = 2*(L*W+W*H+L*H)
362 = 2*(16*3+3*q+16*q)
362 = 2*(48+3q+16q)
362 = 2*(48+19q)
362/2 = 2*(48+19q)/2 ... divide both sides by 2
181 = 48+19q
48+19q = 181
19q+48 = 181
19q+48-48 = 181-48 .... subtract 48 from both sides
19q = 133
19q/19 = 133/19 .... divide both sides by 19
q = 7