Question

The area of the base of a prism is 50 mm2. The perimeter of the base is 30 mm. The height of the prism is 7 mm.

Answer 1

Suppose we have a rectangle with area 50 and perimeter 30. Let's set up equations to find the side lengths.

ab = 50
2a + 2b = 30

Now we need to get one variable alone on one side.

a + b = 15
a = 15 - b

Use substitution and solve.

$a = 15- b\\ (15-b)b = 50 \\ b^2-15b = 50 \\ b^2-15b+50=0 \\ (b-5)(b-10) = 0 \\ \boxed{b=5\ or\ 10}$

So we now know that the square has dimensions 5 and 10. Let's find the surface area.

$SA = 2wl + 2wh + 2lh \\ SA = (2*5*10) + (2*5*7) + (2*10*7) \\ SA = 100 + 70 + 140 \\ \boxed{SA = 310\ u^2}$