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When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square. Determine the missing side length .

When three squares are joined at their vertices to form a right triangle the combined area of the two smaller squares is the same as the area of the largest squ class=

Respuesta :

Lets draw the following picture:

From the figure, we can see that the area of the square on the left is given by

[tex]a^2=225[/tex]

And the area of the square below is

[tex]b^2=8^2=64[/tex]

By applying Pytagorean theorem,

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

we get

[tex]225+64=c^2[/tex]

which gives

[tex]c^2=289[/tex]

therefore, c is equal to

[tex]c=\sqrt[]{289}[/tex]

and the answer is c = 17.

Ver imagen CjG559917