Question

The diagonal of a square measured 7 square root of 2 cm. Find the length of a side of the square

Answer 1

The diagonal of a square measured 7 square root of 2 cm. Then the length of side of square is 7 cm

Solution:

Given that,

The length of diagonal of a square is
`7 √(2)` cm

The figure is attached below

So length of diagonal = AC =
`7 √(2)` cm

Let the length of sides of the square be ‘a’

Since, the diagonal and the sides are forming a right angled triangle

So, we can use Pythagoras theorem,

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

In triangle ABC, AC forms the hypotenuse and BC is the perpendicular and AB is the base

So above Pythagoras theorem definition,

`(\mathrm{BC})^(2)+(\mathrm{AB})^(2)=(\mathrm{AC})^(2)`

`\begin{array}{l}{(a)^(2)+(a)^(2)=(7 √(2))^(2)} \\\\ {2 a^(2)=98} \\\\ {a^(2)=98 / 2=49} \\\\ {a=√(49)=7}\end{array}`

Hence, the length of the square is 7 cm