Question

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?

Answer 1

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 refused (x >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