A foothpath of uniform width runs all around the outside of a rectangular field of 30 M long and 24 M wide . If the path occupies an area of 360 square metre square,find its width.
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Answered by
11
let the width be x
(24)2x + (30)2x + 4x^2 =360
48x + 60x + 4x^2=360
x^2+27x-90=0
x^2+30x-3x-90=0
(x+30)(x-3)=0
x=3m=width
(24)2x + (30)2x + 4x^2 =360
48x + 60x + 4x^2=360
x^2+27x-90=0
x^2+30x-3x-90=0
(x+30)(x-3)=0
x=3m=width
Ganny1:
is it correct
Why you have multiplied 24with 2x and 30 with 2x ?
Why you have not added 2x inspite of multiplying ?
because path is on both sides so instead of 24x+24x I multiplied it with two
Answered by
0
Step-by-step explanation:
Let the width of the path be x.
∴ length of the rectangular field and path =2x+30
and breadth =2x+24
Area of rectangular field =(30×24)
=720
Area of the rectangular field and path =(2x+30)(2x+24)
Now,
(2x+30)(2x+24)−720=360
⇒4x
2
+48x+60x+720−720=360
⇒4x
2
+108x−360=0
⇒x
2
+27x−90=0
⇒x
2
+30x−3x−90=0
⇒x(x+30)−3(x+30)=0
⇒(x+30)(x−3)=0
⇒x=−30 and x=3
Negative value is not valid,
∴ Width is 3 cm
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