Question

What is the algebraic expression for the area of the wall to be painted?​

Answer 1

Answer:

-5x² + 50x + 10

Step-by-step explanation:

Area to paint= Total area of the wall - Area of window - Area of door

Total area of the wall:

(5x + 1) × 10

= 50x + 10

Area of window = 2x²

Area of door = 3x²

∴ Area to paint = 50x + 10 -  2x² -  3x²

= -5x² + 50x + 10

Answer 2

• (50x + 10 - 5x²) unit² .

Given :- Refer to image .

To Find :- The algebraic expression for the area of the wall to be painted ?

Formula used :-

• Area of rectangle = Length × Breadth.

Solution :-

Wall :-

→ Length = (5x + 1) unit

→ Breadth = 10 unit

So,

→ Area of wall = Length × Breadth = (5x + 1) × 10 = 10(5x + 1) unit² ---------- Equation (1)

Door :-

→ Length = x unit

→ Breadth = 3x unit

So,

→ Area of wall = Length × Breadth = x × 3x = 3x² unit² ---------- Equation (2)

Window :-

→ Length = 2x unit

→ Breadth = x unit

So,

→ Area of wall = Length × Breadth = 2x × x = 2x² unit² ---------- Equation (3)

then,

→ Area of wall that was painted = Area of wall - (Area of door + Area of window) = Equation (1) - [Equation (2) + Equation (3)]

→ Required area to be painted = 10(5x + 1) - (3x² + 2x²)

→ Required area to be painted = 10(5x + 1) - 5x²

→ Required area to be painted = 5{2(5x + 1) - x²}

→ Required area to be painted = 5(10x + 2 - x²)

→ Required area to be painted = (50x + 10 - 5x²) unit² .

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