All sides of a square are equal, right? So if you split the square with a diagonal, you’ll get two isosceles triangles. If two sides of a triangle are equal, then the opp. angles are also equal. Since one angle of a square is 90 degrees, the other two equal angles must be 45 and 45 degrees. This is a 45-45-90 triangle, which means that the two legs are equal and the hypotenuse is the value of a leg times √2. Since the side of the square is 5, the hypotenuse (diagonal) is 5√2.
Step-by-step explanation:
let ABCD a square.
in triangle ABC
angle B = 90°
BY pythagoras
(AC)²= (AB)²+(BC)²
(AC)²= (5)² + (5)²
(AC)²= 50
AC=√50
AC= 5√2
ANS 🙂
Answer:
5 √2
Step-by-step explanation:
All sides of a square are equal, right? So if you split the square with a diagonal, you’ll get two isosceles triangles. If two sides of a triangle are equal, then the opp. angles are also equal. Since one angle of a square is 90 degrees, the other two equal angles must be 45 and 45 degrees. This is a 45-45-90 triangle, which means that the two legs are equal and the hypotenuse is the value of a leg times √2. Since the side of the square is 5, the hypotenuse (diagonal) is 5√2.