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.Com
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) (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:
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
RELATED QUESTIONS
Find the total surface area of a right prism whose bases are regular hexagons with sides... (answered by ikleyn)
What is the volume of the right prism with height h=14 cm, if the base of the prism is a... (answered by ikleyn)
The hypotenuse of a right triangle is 26 millimeters. One leg of the right triangle is 10 (answered by addingup)
a rectangular prism has height 4 millimeters and width 5 millimeters.If the total surface (answered by bucky)
Find the surface area of the regular pyramid.
A triangular pyramid. The base triangle... (answered by ikleyn)
In a right triangle, a and b are the lengths of the legs and c is the length of the... (answered by Cromlix)
In an right triangle prism the triangular base ABC is right angled at B,AB=5x cm and... (answered by greenestamps)
What is the area of a right triangle with a hypotenuse of 68 millimeters and a leg of 60... (answered by nerdybill)
A right triangle has an area of 60 square millimeters. One leg has a length of 6... (answered by rfer)