a rectangular carpet has an area 120sq.m and perimeter 46m. the length of the diaganol is
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AnswEr :
- Area of Rectangular Carpet is 120 m²
- Perimeter of Carpet is 46 m
- Find the length of Diagonal.
Let the length be l m and, breadth be b m.
• According to the Question Now :
⇒ Area = Length × Breadth
⇒ 120 = l × b
⇒ b = 120 / l⠀⠀⠀⠀⠀⠀—eq.( I )
⇒ Perimeter = 2( Length + Breadth)
⇒ 46 = 2(l + b)
- Dividing Both term by 2
⇒ 23 = (l + b)
- putting the vale of b from eq.( I )
⇒ 23 = l + 120 / l
⇒ 23 = ( l² + 120 ) / l
⇒ 23l = l² + 120
⇒ l² - 23l + 120 = 0
⇒ l² - 15l - 8l + 120 = 0
- by middle term splitting
⇒ l(l - 15) - 8(l - 15) = 0
⇒ (l - 8)(l - 15) = 0
⇒ l = 8 m ⠀or, ⠀l = 15 m
◗ b = 120 / l = 120 / (8 or, 15) = 15 m or, 8 m
So, we can take length and breath to any of the measurement i.e. either 15 m or 8 m.
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• Diagonal of the Carpet :
⇒ Diagonal = √(l² + b²)
⇒ Diagonal = √(8² + 15²)
⇒ Diagonal = √(64 + 225)
⇒ Diagonal = √289
⇒ Diagonal = 17 m
∴ Therefore, Diagonal will be 17 metre.
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