Question

he 45°-45°-90° triangle theorem
ngth of the hypotenuse of a 45°-45°-90° triangle with legs that are 8 cm long?

• according to the theorem, the

__________ is the length of each leg
times √____ . so that would be 8√2 ,

• check using the pythagorean theorem

a² + b² = c²
8² + 8² = c²
____ + 64 = c²
128 = c²
√128 = √c²
√128 = c
√64(2) = c
√ = c

Explanation:

Step1: Recall 45-45-90 Triangle Theorem

In a \(45^\circ - 45^\circ - 90^\circ\) triangle, the hypotenuse \(c\) is the length of each leg times \(\sqrt{2}\). So first blank: hypotenuse, second blank: \(2\).

Step2: Calculate \(8^2\)

\(8^2 = 64\), so the blank in \(8^2 + 8^2 = c^2\) expansion is \(64\) (since \(8^2 = 64\), so \(64 + 64 = c^2\)).

Step3: Simplify \(\sqrt{128}\)

Factor \(128\) as \(64\times2\). Then \(\sqrt{64\times2}=\sqrt{64}\times\sqrt{2}=8\sqrt{2}\). So the blanks are \(8\) and \(2\).

Answer:

First part blanks: hypotenuse, \(2\); Second part blank: \(64\); Third part blanks: \(8\), \(2\) (Final simplified hypotenuse: \(8\sqrt{2}\) cm)