Question

This square has the hypotenuse of a right triangle as one of its sides.

Answer 1

Answer:

$A=2 square units$

Step-by-step explanation:

It is given that square has the hypotenuse of a right triangle as one of its sides.

Thus, in order to find the hypotenuse of the square, we use the Pythagoras theorem, that is

$c^2=a^2+b^2$

⇒$c^2=(1)^2+(1)^2$

⇒$c^2=1+1$

⇒$c^2=2$

⇒$c=\sqrt{2}units$

Therefore, the length of the hypotenuse will be ${\sqrt{2}}$.

Now, since square has all the sides of equal measure, therefore the measure of the sides of the square will be ${\sqrt{2}}$units.

Now, Area of square is given as:

$A=(side)^2$

$A=(\sqrt{2})^2$

$A=2 square units$

Thus, the area of square is $2 square units$.

Answer 2

Since the legs of the triangle are 1 and 1 the hypotenuse would be 1 also. And since squares have equal sides you know that every other side of the square are 1. The algorithm for area is base times height. So 1 times 1 is 1 unit squared.<span />