Question

Find the length of the side of a square if the length of its diagonal is 10 cm.

Answer 1

From the question it is given that,

Length of Diagonal = 10 cm

Let us assume square ABCD.

Sides AB = y, BC = y, CD = y, DA = y

Diagonal AC = 10 cm

Now, consider triangle ABC

By the rule of Pythagoras theorem,

AC² = AB² + BC²

10² = y² + y²

100 = 2y²

y² = 100/2

y² = 50

y = √50 cm

y = 5√2 cm

∴The length of the side of square is √50 cm or 5√2.