## 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 r

Question

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.

in progress
0

Math
1 month
2021-08-18T05:40:45+00:00
2021-08-18T05:40:45+00:00 2 Answers
0 views
0
## Answers ( )

AnswerLength of the rectangle = 18 cm

Breadth of the rectangle = 15 cm

Area of the rectangle = 270 cm²

GivenThe 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 FindDimensions of original rectangle

Area of the rectangle

Point to be notedArea of rectangle = Length × Breadth

⇒ A = lb

SolutionLet 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 =

xyA/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 cmOn sub. x value in (1) , we get ,

⇒ (18) – y = 3

⇒ y = 18 – 3

⇒

y = 15 cmSo , Area of the rectangle =

xy = 270 cm²Answer: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