Answer:
1. Using the Pythagorean theorem.
2. Using the ratio 1 : 1 : √2.
Step-by-step explanation:
There are two options to find the value of x:
1. Using the Pythagorean theorem:
Hypotenuse = 5√2 inches and legs are equal in a 90 - 45 - 45 triangle like this.
Hypotenuse² = Leg² + Leg²
(5√2)² = 2Leg²
50 = 2Leg²
50/2 = Leg²
Leg² = 25
√Leg² = √25
Leg = 5 inches ⇒ x = 5
2. Using the ratio 1 : 1 : √2, this way:
1 : 1 : √2
x : x : 5√2
x = 5√2/√2
x = 5 and let's recall that in a 90 - 45 - 45 triangle legs are equal, therefore. ratio is:
5 : 5 : 5√2
