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

The estimated value of the length of the hypotenuse is units. The estimated value of the area of the square is square units.

(Hint: The hypotenuse is the side opposite the right angle. To find the hypotenuse of a right triangle, use the Pythagorean Theorem, c2= a2 + b2.)

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.

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boffeemadrid boffeemadrid · Answer 2 · 2019-05-22T08:25:37+02:00

Answer:

[tex]A=2 square units[/tex]

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

[tex]c^2=a^2+b^2[/tex]

⇒[tex]c^2=(1)^2+(1)^2[/tex]

⇒[tex]c^2=1+1[/tex]

⇒[tex]c^2=2[/tex]

⇒[tex]c=\sqrt{2}units[/tex]

Therefore, the length of the hypotenuse will be [tex]{\sqrt{2}}[/tex].

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

Now, Area of square is given as:

[tex]A=(side)^2[/tex]

[tex]A=(\sqrt{2})^2[/tex]

[tex]A=2 square units[/tex]

Thus, the area of square is [tex]2 square units[/tex].