In a [tex]\(45^{\circ}-45^{\circ}-90^{\circ}\)[/tex] triangle, the lengths of the legs are equal, and the hypotenuse is related to the legs by a simple relationship. Specifically:
1. Each leg of the triangle has the same length, which is given as 14 cm.
2. The hypotenuse of a [tex]\(45^{\circ}-45^{\circ}-90^{\circ}\)[/tex] triangle can be determined using the formula where the hypotenuse is [tex]\( \text{leg length} \times \sqrt{2} \)[/tex].
Given the leg length [tex]\( \text{leg length} = 14 \text{ cm} \)[/tex]:
To find the hypotenuse:
- Multiply the leg length by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[ \text{Hypotenuse} = 14 \times \sqrt{2} \text{ cm} \][/tex]
[tex]\[ \text{Hypotenuse} = 14 \sqrt{2} \text{ cm} \][/tex]
Thus, the length of the hypotenuse is [tex]\( 14 \sqrt{2} \)[/tex] cm.
Let's match this result to the options given:
- 7 cm
- [tex]\( 7\sqrt{2} \)[/tex] cm
- 14 cm
- [tex]\( 14\sqrt{2} \)[/tex] cm
Clearly, the correct answer is [tex]\( 14\sqrt{2} \)[/tex] cm.
