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The surface area S of a rectangular prism with length ℓ, width w, and helght h is S=2(lw+wh+lh). Which expression is equivalent to the height, h ?

The surface area S S of a rectangular prism with length ℓ \ell , width w w , and helght h h is S=2(lw+wh+lh) S=2(l w+w h+l h) . Which expression is equivalent to the height, h h ?

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Q. The surface area S S of a rectangular prism with length ℓ \ell , width w w , and helght h h is S=2(lw+wh+lh) S=2(l w+w h+l h) . Which expression is equivalent to the height, h h ?
  1. Isolate terms with h: Start by isolating the terms involving h h in the surface area formula.\newlineGiven: S=2(lw+wh+lh) S = 2(lw + wh + lh) \newlineDivide both sides by 22 to simplify:\newlineS2=lw+wh+lh \frac{S}{2} = lw + wh + lh
  2. Simplify by dividing: Rearrange the equation to isolate terms with h h .\newlineS2−lw=wh+lh \frac{S}{2} - lw = wh + lh \newlineFactor out h h from the right side:\newlineS2−lw=h(w+l) \frac{S}{2} - lw = h(w + l)
  3. Rearrange to isolate h: Solve for h h by dividing both sides by w+l w + l .\newlineh=S2−lww+l h = \frac{\frac{S}{2} - lw}{w + l}

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