Question

In the diagram, AB, BC, CD, DE, EF, FG, GH, and HK all have lengths 4, and all angles are right angles, with the exception of the angles at D and F.



Determine the length of DF.

Answer 1

Answer:

5.66 length (3s.f.)

Step-by-step explanation:

$\sqrt{4 {}^{2} + 4 {}^{2} }$

= 5.65685

= 5.66 (3 s.f.)

Answer 2

By using the Pythagorean theorem, we will see that the length of DF is 5.7 units.

How to get the length of DF?

We can make a right triangle with the sides: DE, FE, and DF.

Such that we know that:

DE = FE = 4

These two are the cathetus of the right triangle.

Then DF is the hypotenuse.

Now, remember the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse, then we have:

(DE)^2 + (FE)^2 = (DF)^2

4^2 + 4^2 =(DF)^2

√32 = DF = 5.7

The length of DF is 5.7 units.

If you want to learn more about right triangles, you can read:

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