The breadth of a rectangle is 3 less than the length. If both the length and the breadth are reduced by 3 units, the area of the rectangle reduces by 90sq. units. Find the dimensions of the original rectangle and also the area.
Answers
Answer:
l = 18 units, b = 15 units
Step-by-step explanation:
Let the length be l, and breadth be b.
Given, b = l - 3
So, area = lb = l(l-3) = l^2 - 3l
When length and breadth are reduced by 3 units, then new length and breadth = (l-3) and (b-3) or (l-6) units.
Given, (l-3)(l-6) = l^2 - 3l - 90
l^2 - 9l + 18 = l^2 - 3l - 90
6l = 108
l = 18 units.
b = l - 3 = 18 - 3 = 15 units
Answer
Length of the rectangle = 18 cm
Breadth of the rectangle = 15 cm
Area of the rectangle = 270 cm²
Given
The breadth of a rectangle is 3 less than the length. If both the length and the breadth are reduced by 3 units, the area of the rectangle reduces by 90 sq. units.
To Find
Dimensions of original rectangle
Area of the rectangle
Point to be noted
Area of rectangle = Length × Breadth
⇒ A = lb
Solution
Let the length of the rectangle be , " x "
Breadth be , " y "
A/c , " The breadth of a rectangle is 3 less than the length "
⇒ y = x - 3
⇒ x - y = 3 ... (1)
Area of the rectangle = xy
A/c , " If both the length and the breadth are reduced by 3 units, the area of the rectangle reduces by 90 sq. units "
⇒ ( x - 3 )( y - 3 ) = xy - 90
⇒ xy - 3x - 3y + 9 = xy - 90
⇒ 3x + 3y = 99
⇒ x + y = 33 ... (2)
Solve (1) + (2) ,
⇒ ( x - y ) + ( x + y ) = 3 + 33
⇒ x - y + x + y = 36
⇒ 2x = 36
⇒ x = 18 cm
On sub. x value in (1) , we get ,
⇒ (18) - y = 3
⇒ y = 18 - 3
⇒ y = 15 cm
So , Area of the rectangle = xy = 270 cm²