(1) 40 मी x 30 मी मापे असलेल्या एका आयताकृती बागेच्या सभोवती समान
रुंदी असलेली एक पायवाट बांधलेली आहे. जर त्या पायवाटेचे क्षेत्रफळ
456 मी' असेल, तर त्या पायवाटेची रुंदी काढा.
Answers
Given:
40 मी x 30 मी मापे असलेल्या एका आयताकृती बागेच्या सभोवती समान रुंदी असलेली एक पायवाट बांधलेली आहे. जर त्या पायवाटेचे क्षेत्रफळ 456 मी' असेल,
A rectangular garden 40 m × 30 m is surrounded from outside by a path of equal width. if the area of the path is 456 m²
To find:
तर त्या पायवाटेची रुंदी काढा.
The width of the path
Solution:
Finding the area of the garden excluding the footpath:
The dimensions of the rectangular garden:
Length = 40 m
Breadth = 30 m
∴ The area of the rectangular garden (excluding footpath) is,
= length × breadth
= 40 × 30
= 1200 m²
Finding the area of the garden including the footpath:
Let "x" be the width of the footpath.
So,
New length = (40 + 2x) m
New breadth = (30 + 2x) m
∴ The area of the garden including the footpath is,
= (40 + 2x)(30 + 2x)
= (1200 + 80x + 60x + 4x²) m
Finding the width of the footpath:
We know,
Area of the footpath = [Area including footpath] - [Area excluding footpath]
⇒ 456 m² = (1200 + 80x + 60x + 4x²) m² - 1200 m²
⇒ 456 = 1200 + 80x + 60x + 4x² - 1200
⇒ 456 = 140x + 4x²
⇒ 4x² + 140x - 456 = 0
⇒ x² + 35x - 114 = 0
⇒ x² + 38x - 3x - 114 = 0
⇒ x(x + 38) - 3(x + 38) = 0
⇒ (x + 38)(x - 3) = 0
⇒ x = - 38 or 3
since the length of the width cannot be in negative
⇒ x = 3
Thus, the width of the path is → 3 m.
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