A rectangle field has an area of 1764 m^2. The width of the field is 13m more than the length. What is the perimeter of the field?

Step-by-step explanation:

hello:

let y the length and x the width

A the area and P the perimeter

so : A = xy and P = 2 (x+y) ... y > x and x >0; y>0

xy = 1764 ... (1)

y = x + 13 ... (2) put this value in (1) : x (x+13) = 1764

x²+13x - 1764 = 0 ... quadratic equation

calculate : Δ = b² - 4ac a = 1 and b = 13 and

c = - 1764

Δ = (13) ² - 4 (1) (-1764) = 169 + 7056 = 7225=85²

X1 = (-b-√Δ) / 2a = (-13-85) / 2 0)

X2 = (-b+√Δ) / 2a = (-13+85) / 2 = 72/2 = 36

so : x = 36 put this value in (2) : y = 36+13 = 49

the perimeter is : P = 2 (x+y)

P = 2 (36+49) = 170 m