Respuesta :

Answer:

289 in^2

Step-by-step explanation:

1. Find side of the small square: (DG=a)

64= a^2

a= 8

2. Find hypotenuse of triangle being formed: (OG=c and DO=b)

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

[tex]8^{2}[/tex] + [tex]15^{2}[/tex] = [tex]c^{2}[/tex]

c= 17

3. Find area of square:

[tex]c^{2}[/tex]= A

(17)*(17)= 289 in^2

The area of the shaded square when the DOG is a right triangle formed by the placement of 3 squares so it should be 289 [tex]in^2[/tex].

Calculation of the area;

Find we have to determine the side of the small square i.e. (DG=a)

Now

64= [tex]a^2[/tex]

So,

a= 8

Now find the hypothenuse

[tex]8^2 + 15^2 = c^2[/tex]

c = 17

Now the area should be like

= (17) (17)

= 289 [tex]in^2[/tex].

Hence, The area of the shaded square when the DOG is a right triangle formed by the placement of 3 squares so it should be 289 [tex]in^2[/tex].

Learn more about an area here: https://brainly.com/question/24417940

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