The perimeter of a square is 54cm. Find the length of a diagonal, rounding to the nearest tenth.
A. 182.3cm
B. 19.1cm
C. 13.5cm
D. 22.4cm

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

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form