Question

The diagonal of a square is 72 cm. Find the side of the square.​

Answer 1

Answer:

let the side of square be x

(side)^2+(side)^2=(diagonal)^2 {Pythagoras theorem}

x^2+x^2=72^2

2x^2=5184

x^2=5184÷2

x=√2592

x=50.91(approx)

Answer 2

The side of the square will be 50.91.

A square consists of 2 congruent right angled triangles joined by their diagonals.

The diagonal of a square can be thought of as the diagonal of the right triangles and as all sides of a square are equal.

By finding one side of an of the triangles we can find the side of the square.

Let the sides of the square be "a".

The sides of the right triangles will also be "a" as the square is made from them.

From pythagoras theorem we know that sum of squares of sides of a right angled triangle = square of its diagonal.

=> ("a")^2 + ("a")^2 = (72)^2 ( by pythagoras theorem)

=> 2("a")^2=(72)^2

Hence we get a as 50.91(properties of algebra and square root).