Triangle town wants to build a school that is equidistant from its three cities L, M, and N. Which construction correctly finds
the best location of the school?
Option choices are...
A. Construction Y because point E is the incenter of ΔLMN
B. Construction Y because point E is the circumcenter of ΔLMN
C. Construction X because point C is the incenter of ΔLMN
D. Construction X because point C is the circumcenter of ΔLMN
Option choices are...
A. Construction Y because point E is the incenter of ΔLMN
B. Construction Y because point E is the circumcenter of ΔLMN
C. Construction X because point C is the incenter of ΔLMN
D. Construction X because point C is the circumcenter of ΔLMN
1 answer:
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Refer to the attachment for the diagram of the problem.
Let us call the two identical sides of the isosceles triangle with s. Since we know that the hypotenuse measures 45 inches, we can find s by using the Pythagorean Theorem:
We can notice that the figure will have similar triangles with the smaller triangle having one length equal to 5x. We then compute for the equivalent hypotenuse of the smaller triangle (denoted as y).
We can then solve for the value of x by applying the Pythagorean Theorem in the smaller triangle.
We ignore the negative value since there is no negative side. x is therefore 4.55 thus the dimensions of the rectangle would be 22.75 and 9.1. For the other case, the dimensions would simply be inverted since we would be dealing with a rectangle with its width longer than its length.
Let us call the two identical sides of the isosceles triangle with s. Since we know that the hypotenuse measures 45 inches, we can find s by using the Pythagorean Theorem:
We can notice that the figure will have similar triangles with the smaller triangle having one length equal to 5x. We then compute for the equivalent hypotenuse of the smaller triangle (denoted as y).
We can then solve for the value of x by applying the Pythagorean Theorem in the smaller triangle.
We ignore the negative value since there is no negative side. x is therefore 4.55 thus the dimensions of the rectangle would be 22.75 and 9.1. For the other case, the dimensions would simply be inverted since we would be dealing with a rectangle with its width longer than its length.
