contestada

Angle $eab$ is a right angle, and $be = 9$ units. what is the number of square units in the sum of the areas of the two squares $abcd$ and $aefg$?

Respuesta :

nobillionaireNobley
Let the measure of side AB be x, then, the measue of side AE is given by

[tex]AE=\sqrt{9^2-x^2}[/tex].

Now, ABCD is a square of size x, thus the area of square ABCD is given by

[tex]Area=x^2[/tex]

Also, AEFG is a square of size [tex]\sqrt{9^2-x^2}[/tex], thus, the area of square AEFG is given by

[tex]Area=\left(\sqrt{9^2-x^2}\right)^2=9^2-x^2=81-x^2[/tex]

The sum of the areas of the two squares ABCD and AEFG is given by

[tex]x^2+81-x^2=81[/tex]

Therefore, the number of square units in the sum of the areas of the two squares ABCD and AEFG is 81 square units.

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