SOLUTION: Right triangle ABC with legs AB= 9 millimeters and BC= 12 millimeters is the base of a right prism that has a surface area of 450 square millimeters. What is the height of the pris

Algebra ->  Triangles -> SOLUTION: Right triangle ABC with legs AB= 9 millimeters and BC= 12 millimeters is the base of a right prism that has a surface area of 450 square millimeters. What is the height of the pris      Log On


   

Question 604437: Right triangle ABC with legs AB= 9 millimeters and BC= 12 millimeters is the base of a right prism that has a surface area of 450 square millimeters. What is the height of the prism?
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that AB is perpendicular to BC
because it's a triangle, then area of triangle:
Area = 1/2 * base * height
Area = 1/2 * 12 * 9 = 6 * 9 = 54 square milimeters

because it's a right triangle, then we can use Phytagoras theorem to find the other side of the triangle:
AB%5E2+%2B+BC%5E2+=+AC%5E2
9%5E2+%2B+12%5E2+=+AC%5E2
9%5E2+%2B+12%5E2+=+AC%5E2
81+%2B+144+=+AC%5E2
225+=+AC%5E2
AC+=+sqrt%28225%29
AC = 15 milimeters

Surface Area (SA) of a prism:
SA = 2*base area + base perimeter*prism's height
450 = 2*54 + (9 + 12 + 15)*prism's height
450 = 108 + 36*prism's height
450 - 108 = 36*prism's height
342 = 36 * prism's height
prism's height = 342/36 = 9.5 milimeters

so, the height of the prism is 9.5 millimeters