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Step-by-step explanation:
Area of flowers bed = 260m²(given)
Width of path = x
Length of flowers bed = 28-2x
Width of flowers bed =12-2x
Area of flowers of bed =length of flower bed * width of flowers bed
(28-2x)(12-2x)=260
336-24x-56x+4x²=260
4x²-80x+76=0
x²-20x+19=0
x²-19x-x+19=0
x(x-19)-1(x-19)=0
(x-19)(x-1)=0
Roots will be
x-19=0; x=19
x-1=0;x =1
When, x=1
Length of flowers bed = 28-2x =28-2(1)=26m
Length of flowers bed = 26m
Width of flowers bed =12-2x=12-2(1)=10 m
Width of flowers bed =10 m
Solutions:-
1)
Width of path x= 1 m
2)
Length of flowers bed = 26m
Length of flowers bed = 26mWidth of flowers bed =10 m
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