Question

put the steps in order: 45 - 45 - 90
solve for x by putting the steps in order
checker: ✗
short / long = short / long
4.2 units = x
3√2 = x
3√2 = 1·x
3/x = 1/√2

Explanation:

Step1: Set up the proportion

In a \(45 - 45-90\) triangle, the ratio of the side to the hypotenuse is \(\frac{\text{short}}{\text{long}}\). If the leg (short side) is \(3\) and the hypotenuse is \(x\), we have \(\frac{3}{x}=\frac{1}{\sqrt{2}}\) (using the property of \(45 - 45-90\) triangles where leg : hypotenuse \(=1:\sqrt{2}\)).

Step2: Cross - multiply

Cross - multiplying \(\frac{3}{x}=\frac{1}{\sqrt{2}}\) gives \(3\sqrt{2}=1\times x\).

Step3: Simplify

Since \(3\sqrt{2}=1\times x\), then \(x = 3\sqrt{2}\).

Answer:

1. \(\frac{3}{x}=\frac{1}{\sqrt{2}}\)
2. \(3\sqrt{2}=1\times x\)
3. \(3\sqrt{2}=x\)