Question

the lenght of a rectangle is 5 cm less than twice in its breadth if the length is decreased by 3 cm and breadth increased by 2 cm the perimeter of the resulting rectangle is 72 cm find the area of original rectangle​

Answer 1

ANSWER:

AREA OF RECTANGLE!

FORMULAE TO BE USED:

Area of the rectangle=Length×breadth

Given:

• the lenght of a rectangle is 5 cm less than twice in its breadth.

• if the length is decreased by 3 cm and breadth increased by 2 cm the perimeter of the resulting rectangle is 72 cm.

To find:

the area of original rectangle

Assumptions:

Let the length of the rectangle be x cm.

Let the breadth of the rectangle be y cm.

Solution:

According to the first statement,

the lenght of a rectangle is 5 cm less than twice in its breadth

the length of a rectangle = x

is 5 cm less = -5

than twice its breadth = 2y

So, the equation forms as,

x = 2 (y-5)------>1

According to the second statement,

if the length is decreased by 3 cm and breadth increased by 2 cm the perimeter of the resulting rectangle is 72 cm.

if the length is decreased by 3cm =2(x-3)

and breadth is increased by 2cm=2(y+2)

the perimeter of the resulting rectangle is 72 cm= 2(l+b)=72

So, this equation forms as,

2(x-3) + 2 (y+2)=72

2x - 6 + 2y + 4 = 72

2x + 2y +4 - 6 = 72

2x + 2y - 2 = 72 ------>2

÷ throughout equation (2) by 2

x + y - 1 = 36

x + y = 36 + 1

x + y = 37 ------> 3

Now, to find the breadth of the rectangle substitute the value of x from equation (1) in equation (3)

(2y - 5) + y = 37

2y - 5 + y =37

3y = 37 + 5

3y = 42

y = 42/3

y = 14

As in our assumptions we assumed y to be the breadth of the rectangle, therefore, the breadth of the rectangle is 14 cm.

Now, let's find the value of x i.e the length of the rectangle.

Put y = 14 in equation (1) to find the value of x.

x = 2 (14) - 5

x = 28 - 5

x = 23.

According to the assumptions x is the length of the rectangle which is 23 cm.

.•.length of the rectangle(x) = 23cm

breadth of the rectangle(y)=14 cm.

As per the question we are asked to find the area of the rectangle, so we can now easily calculate the area of the rectangle using the formula:

Area of the rectangle = Length × breadth

Where length = x = 23cm

and breadth = y = 14 cm

.•. Area of the rectangle = x × y

Area of the rectangle = 23 × 14

.•. Area of the rectangle = 322cm²

Length of the rectangle = 23cm

Breadth of the rectangle = 14cm

Area of the rectangle = 322 sq.cm