Question

the length and breadth of a rectangle are 10 centimetres and 4 centimetres it is made larger increasing the length and breadth of by the same amount find all the algebraic expressions for the area and perimeter of the enlarged rectangle respectively. and can we use same algebraic expression for both expression justify

Proper answer needed please ​

Answer 1

Answer:

Step-by-step explanation:

Length = 10 cm

Breadth = 4 cm

increase = x cm

New length = 10 + x cm

New breadth = 4 + x cm

Area = Length * breadth

( 10 + x ) * ( 4 + x )

10 ( 4 + x ) + x ( 4 + x )

40 + 10x + 4x + x²

x² + 14x + 40 = Area

Perimeter = 2 ( length + breadth )

= 2 ( 10 + x + 4 + x )

= 2 ( 2x + 14 )

= 4x + 28 cm

No we cant use the same algebraic expression for both as both have different dimensions

#answerwithquality #BAL

Answer 2

Given : Length of the rectangle = 10 cm

Breadth of the rectangle = 4 cm

Solution : Let the length and the breadth increase by x cm.

Therefore the new length of the rectangle = (10 + x) cm

New breadth of the rectangle = (4 + x) cm

Now, Perimeter of the enlarged rectangle

⇒2 (Length + Breadth)

⇒2(10 + x + 4 + x) cm

⇒2(2x + 14) cm

⇒ (4x + 28) cm

Area of the enlarged rectangle

= Length × Breadth

⇒ (10 + x) × (4 + x) cm²

⇒ 10(4 + x) + x(4 + x) cm²

⇒ (40 + 10x + 4x + x²) cm²

⇒ [40 + (10 + 4)x + x²] cm²

⇒ (40 + 14x + x²) cm²

Thus, the algebraic expressions for the area and perimeter of the enlarged rectangle are 40 + 14x + x2 and 4x + 28 respectively.

Now, let the length and breadth decrease by x cm.

∴ New length of rectangle = (10 − x) cm

New breadth of rectangle = (4 − x) cm

Perimeter of the new rectangle.

= 2 (Length + Breadth)

⇒ 2 (10 − x + 4 − x) cm

⇒ 2(14 − 2x) cm

⇒(28 − 4x) cm

Area of the new rectangle = Length × Breadth

⇒(10 − x) × (4 − x) cm²

⇒ 10(4 − x) − x(4 − x) cm²

⇒ (40 − 10x − 4x + x²) cm²

⇒ [40 − (10 + 4)x + x²]cm²

⇒ (40 − 14x + x²) cm²

Thus, the algebraic expressions for the area and perimeter of the new rectangle are 40 − 14x + x² and 28 − 4x respectively which are not equal to the algebraic expressions for the area and perimeter of the enlarged rectangle.

Hence, we cannot use the same algebraic expressions in both the cases.