Question

Jules owns a square plot of land that measures 30 yards on each side. He plans to divide the land in half by building a fence, as shown by the dotted line below. How many yards of fencing will Jules need?
a) 15 yd
b) 30 yd
c) 30 square root 2 yd
d) 30 square root 3 yd

Answer 1

we know that

The length of the fence is equal to the length of the diagonal of the square

so

Applying the Pythagoras theorem

$BD^{2} =DC^{2}+BC^{2}$

we have

$DC=BC=30\ yd$

substitute

$BD^{2} =30^{2}+30^{2}$

$BD^{2} =1,800$

$BD=\sqrt{1,800}=30\sqrt{2} \ yd$

therefore

the answer is the option C

$30\sqrt{2} \ yd$

Answer 2

Answer:

Option c is correct

$30\sqrt{2}$ yards of fencing will Jules need

Step-by-step explanation:

Diagonal of square(D) is given by:

$D = \sqrt{2}a$

where a is the length of side of square

As per the statement:

Jules owns a square plot of land that measures 30 yards on each side.

⇒length of each side of square(a) = 30 yards.

As he plans to divide the land in half by building a fence, as shown by the dotted line in the diagram.

Substitute the given values we have;

$D = \sqrt{2} \cdot 30$

⇒$D = 30\sqrt{2}$ yards.

Therefore, $30\sqrt{2}$ yards of fencing will Jules need