Question

A square bathroom has an area of 100m2. What is the distance from

one corner of the bathroom to the opposite corner?

Answer 1

the distance from one corner of the bathroom to the opposite corner is

`10√(2)` meters

Explanation:

A square bathroom has an area of 100m^2

area of the square = side^2

`100=side^2`

side =
`√(100) =10`

To find the distance from one corner of the bathroom to the opposite corner

we find the diagonal of the square

Use pythagorean theorem

c is the hypotenuse , a and b are the sides with length 10 m

`c^2=a^2+b^2`

`c^2=10^2+10^2`

`c=√(200) =10√(2)`

Answer 2

`10√(2)` meters

Explanation:

The bathroom is in the shape of a square. The area of square is given as:

`A=s^2`

Where

s is the length of the side

We know area is 100, thus:

`A=s^2\\100=s^2\\s=√(100) \\s=10`

The side length of the square is 10 meters.

The distance from one corner to another corner is known as the "diagonal".

We use the formula below to get the distance of the diagonal:

`d=√(2)s`

Where

d is the length of diagonal

s is the length of side [here, 10]

THus, length of diagonal is:

`d=√(2)(10)\\ d=10√(2)` meters