+0

# 3d geometry

0
90
2

A rectangular prism has a total surface area of 56.  Also, the sum of all the edges of the prism is 68.  Find the length of the diagonal joining one corner of the prism to the opposite corner.

Apr 19, 2022

#1
+9459
+1

Let L, W, H be the length, width, and height of the prism respectively.

Writing the conditions in mathematical terms,

$$\begin{cases}2(LW + WH + HL) = 56\\4(L + W + H) = 68\end{cases}$$

What we want to find, in mathematical expression, is $$\sqrt{L^2 + W^2 +H^2}$$ by Pythagoras theorem.

Recall the identity: $$(\color{blue}L+W+H\color{black})^2 = \color{red}(L^2+W^2+H^2)\color{black} + \color{green}2(LW + WH + HL)$$

Does this ring a bell?

Apr 19, 2022