SOLUTION: In a certain rectangular prism, the total length of all the edges is 40 and the total surface area is 48. Find the length of the diagonal connecting one corner to the opposite corn

Algebra ->  Surface-area -> SOLUTION: In a certain rectangular prism, the total length of all the edges is 40 and the total surface area is 48. Find the length of the diagonal connecting one corner to the opposite corn      Log On


   

Question 1152808: In a certain rectangular prism, the total length of all the edges is 40 and the total surface area is 48. Find the length of the diagonal connecting one corner to the opposite corner.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let the dimensions of the prism be a, b, and c. Then

(1) The total length of all the edges is 40:
4%28a%2Bb%2Bc%29+=+40 --> a%2Bb%2Bc+=+10

(2) The total surface area is 48:
2ab%2B2ac%2B2bc+=+48

The length we are looking for is the length of the space diagonal of the prism, which is

sqrt%28a%5E2%2Bb%5E2%2Bc%5E2%29

Square equation (1) and substitute equation (2):

%28a%2Bb%2Bc%29%5E2+=+100+=+a%5E2%2Bb%5E2%2Bc%5E2%2B2ab%2B2ac%2B2bc
100+=+a%5E2%2Bb%5E2%2Bc%5E2%2B48
a%5E2%2Bb%5E2%2Bc%5E2+=+100-48+=+52
sqrt%28a%5E2%2Bb%5E2%2Bb%5E2%29+=+sqrt%2852%29+=+2sqrt%2813%29

The length of the diagonal is 2*sqrt(13).