The area of a rectangular hall is 48sq m.If the length and breadth be increased by 1m each, the area is increased by 15sq m. Find the length and breadth of the hall. (please answer step by step)
Answers
Solution
Given :-
- The area of a rectangular hall is 48 m² .
- the length and breadth be increased by 1m each, the area is increased by 15 m² .
Find :-
- Length & Breadth
Explanation
Using Formula
★ Area of rectangle = [Length × Breadth]
Let,
- Length be = x
- Breadth be = y
A/C to question,
(The area of a rectangular hall is 48 m²)
==> Area of rectangle = [ length × breadth]
==> 48 = [x × y]
==> ( x y ) = 48
==> (x y) = 48 ___________(1)
Again,
(the length and breadth be increased by 1m each, the area is increased by 15 m² .)
==> Area of rectangle + 15 = 2 × [ (x+1) + (y+1)]
==> (x y) + 15 = [ (x + 1)( y + 1)]
==> (x+1)(y+1) - xy = 15 ________(2)
Keep value by equ(1)
- x = 48/y
==> [ (24/y + 1)(y+1) ] - 48/y × y = 15
==> (24/y + 1)(y+1) = 15 + 48
==> (24/y + 1)(y+1) = 63
==> 24 + y + 24/y + 1 = 63
==> 24/y + y = 63 - 25
==> y² - 14y + 48 = 0
==> y² - 8y - 6y + 48 = 0
==> y(y-8)-6(y-8) = 0
==> (y-8)(y-6) = 0
==> y = 8 Or, y = 6
Keep value of y in equ(1)
When, y = 8
==> x = 48/8
==> x = 6
When, y = 6
==> x = 48/6
==> x = 8
Since,
Length be always be greater than breadth
Hence
- Length & breadth will be = 8 , 6
_________________
Step-by-step explanation:
Assume that the length is x and breadth is y.
As per given condition,
Case 1)
→ xy = 48
→ x = 48/y
Case 2)
→ (x + 1)(y + 1) = 15 + xy
→ xy + x + y + 1 - xy = 15
→ x + y + 1 = 15
→ 48/y + y = 14
→ 48 + y² = 14y
→ y² - 14y + 48 = 0
→ y² - 8y - 6y + 48 = 0
→ y(y - 8) - 6(y - 8) = 0
→ (y - 6)(y - 8) = 0
→ y = 6, 8
Take y as 6 then x = 48/6 = 8
Take y as 8 then x = 48/8 = 6
Hence, the length and breadth of the hall is 8 m and 6 m or 6 m and 8 m.