Question

A right rectangular prism is shown. Find the length of DH to the nearest tenth of an inch. Drag and drop the answer into the box

Answer 1

DH=√(1.5^2+1^2+3^2)

DH=√12.25

DH=3.5in  (exactly, not rounded)

Notice that this is just the three dimensional version of Pythagorean Theorem...

d^2=x^2+y^2+z^2

Answer 2

Answer:  The length of DH is 3.5 in.

Step-by-step explanation:  A rectangular prism ABCDEFGH is shown in the given figure, where

AD = BC = GF = HE = 1.5 in.,  

AB = CD = EF = GH = 1 in.,

AG = DF = BH = CE = 3 in.

We are to find the length of DH.

Let is draw DH and FH as shown in the attached figure.

Then, ΔDHF will be a right-angled triangle with ∠DHF = 90°.

Now, GHFE is a rectangle with length and breadth as follows:

GF = HE = 1.5 in.  and  GH = FE = 1 in.

Since each angle of a rectangle is a right-angle, so ΔGHF will be a right-angled triangle with ∠HGF = 90°.

Using Pythagoras theorem in ΔGHF, we have

$HF^2=GH^2+GF^2\\\\\Rightarrow HF^2=1^2+(1.5)^2\\\\\Rightarrow HF^2=1+2.25\\\\\Rightarrow HF^2=3.25\\\\\Rightarrow HF=\sqrt{3.25}~\textup{in.}$

Again, using Pythagoras theorem in ΔDHF, we have

$DH^2=DF^2+HF^2\\\\\Rightarrow DH^2=3^2+3.25\\\\\Rightarrow DH^2=9+3.25\\\\\Rightarrow DH^2=12.25\\\\\Rightarrow DH=3.5.$

Thus, the length of DH is 3.5 in.