Question

the area of a rectangle is 40 cm²and perimeter is 28 cm.what are its length and breadth​

Answer 1

Answer :—

length : 10 cm

breadth : 4 cm

Solution :—

Given :—

Area : 40 cm²

Perimeter : 28 cm

We know that in a rectangle area is length times breadth and perimeter is twice the sum of length and breadth.

i.e

Area :- L×B

Perimeter :- 2(L+B)

So,

2(L+B) = 28 Perimeter Given

L+B = 14

L= 14-B

L×B = 40 Area Given

(14-B)×B = 40 putting L = 14-B

14B-B²-40 = 0

B²-14B+40 = 0

B²-10B-4B+40 = 0

B(B-10)-4(B-10) = 0

(B-4)(B-10) = 0

B = 4 cm , 10 cm

So, L = 10 cm , 4 cm

if u have to opt for one of these answer. GO for

B = 4 cm

L = 10 cm

as normally we take breadth to be the smaller side

Answer 2

Given :-

• Area of Rectangle = 40 cm²
• Perimeter of rectangle = 28 cm .

To find :-

Length and Breadth of the rectangle .

Formula used :-

• Area of Rectangle = Length × Breadth .
• Perimeter of rectangle = 2( Length × Breadth )

Solution :-

• Let Length of rectangle = x cm .
• also, Breadth of rectangle = y cm .

Therefore, Area of Rectangle = x × y cm²

And,

Perimeter of rectangle = 2( x + y ) .

As we have Area of Rectangle = 40 cm²

Therefore,

x × y = 40 ............eq.(1)

also,

2( x + y ) = 28

divide both side by 2 we get :-

x + y = 14 ...........eq.(2)

From eq.(1)

x × y = 40

x = 40/y

Put the value of x = 40/y in eq.(2) we get :-

$\sf \: \dfrac{40}{y} + y = 14$

$\sf \: \dfrac{40 + {y}^{2} }{y} = 14$

40 + y² = 14y

y² – 14y +40 = 0

Splitting the middle term .

y² – 10y – 4y + 40 = 0

y ( y – 10 ) – 4 ( y - 10 ) = 0

( y - 10 ) ( y - 4) = 0

y - 10 = 0

y = 10

y - 4 = 0

y = 4

Put the value of y = 10 in eq.(2)

x + y = 14

x + 10 = 14

x = 4

Also Put the value of y = 4 in eq.(2)

x + y = 14

x + 4 = 14

x = 10 .

Therefore, When Breadth of rectangle is 10 cm then Length will be 4 cm .

if Breadth of rectangle is 4 cm then Length will be 10 cm .

Some knowledge about Rectangle :-

• Rectangle have to diagonal . both are equal to each other .
• Rectangle have 4 angles all are of 90° .
• Opposite sides of Rectangle are equal and parallel .
• Rectangle can also called parallelogram.