Answer:
36.18 yd and 13.82yd
Step-by-step explanation:
Area of the rectangular tree = Length * Width
A = LW
perimeter of the rectangular tree = 2(L+W)
Given
Area = 500 square yards and
perimeter = 100yards, then;
100 = 2L+2W
50 = L+W .... 1
500= LW ... 2
From 1, W = 50-L
Substitute into 2;
LW =500
L(50-L) = 500
50L-L² = 500
L²-50L + 500 = 0
Factorize
L = 50±√50²-4(500)/2
L = 50±√2500-2000/2
L = 50±√500/2
L = 50±22.36/2
L = 72.36/2 and 27.64/2
L = 36.18 and 13.82
Hence the possible lengths of the tree lot are 36.18 yd and 13.82yd
