the length of rectangle is 1 metre greater than its breadth if the length is increased by 2 metre and the breadth is decreased by 6 the area decreases by 50 metre square what are the dimension of the rectangle
Answers
Answer:
18 m, 17 m
Step-by-step explanation:
Let breadth of rectangle = x.
Then,
Length = x + 1 m.
Area = Length * breadth
= x * (x + 1)
= x^2 + x
Now,
Length is increased by 2 metre and the breadth is decreased by 6.
New Length = x + 1 + 2 = x + 3
New Breadth = x - 6
Area = Length * breadth
= (x + 3) * (x - 6)
= x^2 - 6x + 3x - 18
= x^2 - 3x - 18
But,
Given area decreases by 50 m^2.
=> x^2 - 3x - 18 = x^2 + x - 50
=> x = 17
Thus,
Length = 18 m
Breadth = 17 m
Hope it helps!
EXPLANATION
Let the l breadth of the rectangle be x.
Length= (x+ 1)
Area of rectangle= (x)(x+1) sq metre
According to the question
Length becomes (x+1+2) m when it is increased by 2 metres.
Breadth becomes (x-6) m when decreased by 6 m
(Here, in the second step, in RHS, 50 m is decreased as area is decreased according to the question)
HENCE, Breadth of the rectangle= x= 8 m
Length= x+ 1= 8+1= 9 m