The length of a rectangle exceeds its breadth by 9 CM. if the length and breadth are each increased by 3 cm, the area of the new rectangle will by 84 CM square. more than that of the given rectangle. find the length and breadth of the given rectangle. check your solution.
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Answered by
4
Answer:
17 cm & 8 cm
Step-by-step explanation:
Let breadth = B cm
Length = B+9
Area = B(B+9)
New length = B+9+3 = B +12
New Breadth = B + 3
Area = (B+3)(B+12)
(B+3)(B+12) - B(B+9) = 84
B²+15B+36 - B²-9B= 84
6B = 48
B =8
Length = 8+9 = 17
Answered by
3
Let the breadth of the given rectangle =x cm.
Then its length= (x+9)cm.
Area of the given rectangle =[x(x+9)]cm^2
New breadth=(x+3)cm.
New length =[(x+9)+3]=(x+12).
Area of new rectangle=[(x+3)(x+12)]
(Area of new rectangle)-(area of given rectangle)=84.
=>(x+12)(x+3)-x(x+9)=84.
=>(x^2+15x+36)-x^2-9x=84
=>6x+36=84
=>6x=48
=>x=48/6.
=>x=8 cm.
So, length=(8+9)=17cm.
and breadth = 8cm.
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