Question

The perimeter of a square is 54cm. Find the length of a diagonal, rounding

Answer 1

Answer:

B. 19.1cm

Step-by-step explanation:

Perimeter of a square = 4 × length

Perimeter = 54cm

Perimeter of a square = 4 × length

54 = 4 × length

54 = 4l

Divide both sides by 4

l = 54 / 4

= 13.5cm

Find the length of a diagonal,

Diagonal = hypotenuse

Using Pythagoras theorem

Hypotenuse^2 = opposite^2 + adjacent^2

Opposite = adjacent in a square because of the equal length

Opposite = adjacent = 13.5cm

Hypotenuse^2 = opposite^2 + adjacent^2

= 13.5^2 + 13.5^2

= 182.25 + 182.25

Hypotenuse^2 = 364.5

Find the square root of both sides

√Hypotenuse^2 = √ 364.5

Hypotenuse = 19.09cm

To the nearest tenth = 19.1cm

B. 19.1cm