Question

13 multiple choice 1 point
find the lengths of the missing sides in the triangle. write your answers as
integers or as decimals rounded to the nearest tenth.
not drawn to scale
x = 11.3, y = 8
x = 8, y = 11.3
x = 5.7, y = 6.9
x = 6.9, y = 5.7

Explanation:

Step1: Recall the properties of a 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the legs are equal in length, and the hypotenuse \(c\) is related to the leg \(a\) by the formula \(c = a\sqrt{2}\).

Step2: Analyze the given triangle

Assume the non - hypotenuse sides (legs) are \(y\) and one of the legs (let's say the side opposite the 45° angle which is not labeled in the general 45 - 45 - 90 formula reference). If we assume \(y = 8\) (by looking at the options, we can test the values). Then, if \(y\) is a leg, and using the formula \(x=y\sqrt{2}\) (where \(x\) is the hypotenuse).
Substitute \(y = 8\) into the formula \(x=y\sqrt{2}\). We know that \(\sqrt{2}\approx1.414\). So \(x = 8\times1.414=11.312\approx11.3\).

Answer:

\(x = 11.3,y = 8\) (First option)