Questions: Each leg of a 45°-45°-90° triangle measures 12 cm. What is the length of the hypotenuse? 6 cm 6√2 cm 12 cm 12√2 cm

Transcript text: Each leg of a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle measures 12 cm . What is the length of the hypotenuse? 6 cm $6 \sqrt{2} \mathrm{~cm}$ 12 cm $12 \sqrt{2} \mathrm{~cm}$

Solution

Solution Steps

Step 1: Identify the type of triangle

The given triangle is a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, which means it is a right isosceles triangle. The two legs have equal length, and the angles opposite to them are equal ($45^{\circ}$ each).

Step 2: Recall the relationship between the legs and the hypotenuse

In a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, the ratio of the lengths of the legs to the hypotenuse is $1:1:\sqrt{2}$. If the length of each leg is $x$, the length of the hypotenuse is $x\sqrt{2}$.

Step 3: Calculate the length of the hypotenuse

Given that each leg measures 12 cm, the length of the hypotenuse is $12\sqrt{2}$ cm.