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The areas of the squares adjacent to two sides of a right triangle are shown below.

What is the area of the square adjacent to the third side of the triangle?​

The Areas Of The Squares Adjacent To Two Sides Of A Right Triangle Are Shown BelowWhat Is The Area Of The Square Adjacent To The Third Side Of The Triangle class=

Answer :

CORSAQUIXGO

Answer:

[tex]85\:\mathrm{units^2}[/tex]

Step-by-step explanation:

All side lengths of a square are equal. The three squares create a right triangle, and the hypotenuse of this triangle represents the side length of the square.

All right triangles must follow the Pythagorean Theorem [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the hypotenuse of the triangle.

Therefore, let [tex]h[/tex] be the side length of this largest square. Since the area of a square with side length [tex]s[/tex] is given by [tex]s^2[/tex], [tex]h^2[/tex] will represent the area of the square:

[tex]\sqrt{35}^2+\sqrt{50}^2=h^2=\boxed{85\:\mathrm{units^2}}[/tex]

PRECIOUSPIXIE42GO

Answer:

85

Step-by-step explanation:

We can use the Pythagorean theorem (a^2+b^2=c^2) to find the area of square adjacent to the third side.

Area of a square=side^2

So, we can substitute the areas of the squares that share side lengths with the triangle for a^2, b^2, and c^2 in the Pythagorean theorem.

For example, in the diagram above, the area of the square that shares a side with side length a is 35 square units. So, a^2=35.

Let's fill in the remaining values:

a^2 + b^2 = x^2

35+50-x^2
85=x^2
The area of the square adjacent to the third side of the triangle is 85 units^2.

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