In a 45°-45°-90° triangle, equal legs measure 5√2 cm, how long is the hypotenuse?
In a 45°-45°-90° triangle, the lengths of the legs are equal. Let's call this length "x".
In this case, x = 5√2 cm.
In a 45°-45°-90° triangle, the length of the hypotenuse can be found using the formula c = x√2, where c is the length of the hypotenuse.
Substituting the value of x, we get:
c = 5√2√2
c = 5√(2*2)
c = 5√4
c = 5(2)
c = 10 cm
Therefore, the length of the hypotenuse is 10 cm.
In a 45°-45°-90° triangle, the two legs are congruent, meaning they have the same length. Let's call the length of each leg "x".
The relationship between the lengths of the sides in a 45°-45°-90° triangle is:
leg: leg: hypotenuse = x : x : x√2
Given that the length of each leg is 5√2 cm, we can set up the equation:
x = 5√2
To find the length of the hypotenuse, we substitute the value of x into the formula for the hypotenuse:
hypotenuse = x√2 = (5√2)√2 = 5(√2)(√2) = 5(2) = 10 cm
Therefore, the length of the hypotenuse in the 45°-45°-90° triangle is 10 cm.