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One of Mr. Grayson’s customers, Sarah, is creating an art wall on which she will display some art in triangular frames. She wants three frames, each in the shape of a right triangle.

(a) For the first frame, Sarah already has two wooden pieces that are 17 in. and 22 in. long. Sarah says that since she wants the frame to be a right triangle, there’s only one possible measurement for the last piece of wood. Is Sarah right? If so, what is that last measurement? If not, explain why not and give all possible measurements for the last wood piece. Round to the nearest tenth.

Respuesta :

MrRamon
Sarah is wrong there are two possible measurements for the 3rd piece of wood. 22 could be a leg or the hypotenuse of the triangles. possible measurements include 14.0in and 27.1 in.

The answers can be found by using the Pythagorean theorem.
[tex]a^2+b^2=c^2 [/tex]

1st option 22 is a leg
[tex]17^2+22^2=c^2[/tex]
773=c^2 Square root of both sides
c≈27.1

2nd option 22 is the hypotenuse
[tex]a^2+17^2=22^2[/tex] subtract 17^2 from both sides
a^2=195 Take the square root of both sides
a≈14.0