Answer:
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 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
