Question

the hypotenuse of a 45° - 45° - 90° triangle measures 7√2 units. what is the length of one leg of the triangle? 7 units 7√2 units 14 units 14√2 units

Explanation:

Step1: Recall the properties of a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle

In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the legs are of equal length (\(a\)) and the hypotenuse (\(c\)) is \(a\sqrt{2}\). So, \(c = a\sqrt{2}\).

Step2: Solve for \(a\)

Given \(c = 7\sqrt{2}\), substitute into \(c = a\sqrt{2}\).

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Answer:

7 units