If the side of the square is A units then the diognals of square is _____&units
Answers
Answer:
Length of diagonal of a square = √2 A.
Step-by-step explanation:
Given that we have a square,
Length of each side of square = A
As we know all the angles in a square are right angle i.e. 90 degrees, and a diagonal is formed by joining any two opposite vertices of square so as a result we get a right angled triangle.
As we know that A right triangle satisfies the Pythagoras's theorem which states that
( Hypotenuse )² = (Base)² + (Perperdicular)² ......(1)
In our case
Base = Lenght of side of square = A
Perpendicular = Length side of square = A
Hypotenuse = Diagonal of square
Putting all the values in equation (1)
( Hypotenuse )² = (A)² + (A)²
( Hypotenuse )² = A² + A²
( Hypotenuse )² = 2A²
taking square root on both sides
Diagonal of square = √2 A
So, the length of diagonal of a square having side length A is √2 A.
Answer:
(√2)A units
Step-by-step explanation:
Define x:
Let x be the length of the diagonal.
Explanation:
The 2 sides of the square and the diagonal forms a right angle triangle.
Since it is a right angle triangle, we can use Pythagorean theorem to find the length of the hypotenuse.
Solve x:
A² + A² = x²
2A² = x²
x = (√2)A
Answer: The hypotenuse is (√2)A units
