Question

Select the correct answers. If sides BD and DC have the same length, what is the length of side BC?

Answer 1

Hello! The answer is 4. We know this by:

Because BD and DC are equal we only need to find the length of BD and plug it into the pythagorean theory. (a²+b²=c² where c is the hypotenuse.)

So we find BD by using the pythagorean theory. BA = a and AD=b and BD=c. Plug it all in and we get 1²+1²=BD². We get 2=BD, now we need to take the square root of 2 to get 1.414213562.

Now that we know BD we also know DC so we can plug them into to this: BD² +DC²=BC².

1.414213562²+1.414213562²=4 and the square root of that is 2.

I hope this helped!

Answer 2

Answer:  The correct option is (C) 2 units.

Step-by-step explanation:  Given that the sides BD and DC have the same length in the quadrilateral ABCD.

We are to find the length of side BC.

From the figure, we note that

triangle ABD is a right-angled triangle with BD as the hypotenuse. So, using Pythagoras theorem, we get

$BD^2=AB^2+AD^2\\\\\Rightarrow BD^2=1^2+1^2\\\\\Rightarrow BD^2=1+1\\\\\Rightarrow BD^2=2\\\\\Rightarrow BD=\sqrt2~\textup{units}.$

Now, according to the given information, we have

$BD=DC=\sqrt2~\textup{units}.$

Again, triangle BCD is a right-angled triangle with BC as the hypotenuse. So, using Pythagoras theorem, we get

$BC^2=BD^2+DC^2\\\\\Rightarrow BC^2=(\sqrt2)^2+(\sqrt2)^2\\\\\Rightarrow BC^2=2+2\\\\\Rightarrow BC^2=4\\\\\Rightarrow BC=\sqrt4\\\\\Rightarrow BC=2~\textup{units}.$

Thus, the length of side BC is 2 units.

Option (C) is CORRECT.