Question

8. Every JNV of INDIA has a beautiful Mathematical Garden in one of the INVs, in mathematica garden, there is a wall of a room having a window and a door is displayed in a rectangular chest with the following dimensions as shown below: 5x+1 2x 3x Dood Window 10 1 (1) What is the algebraic expression for the area of the wall to be painted? दिवार के क्षेत्रफल का बीजगणितीय व्यंजक होगा - (A) 5x (2x +1) sq. units (C) (25x+10) sq units (B) 10x (2x+1) sq units (D) (20x--10) sq units 1 Choose the correct expression for the area of door- दरवाजा के क्षेत्रफल का सही उत्तर चुनिए (A) 9x sq. units (B) 15x'sq. units (C) 10x-sq. units (D) 3x sq. units 1 Which of the following expression represents the perimeter of the wall? दिवार के परिमाप का व्यंजक निम्न में से कौन है (A) 3(5x-1) units (B) 5 (5x-1) units (C) 4(5x+1) sq. units (D) none of these, (iv) I Which of the following expression represents the perimeter of the window खिड़की के परिमाप का व्यंजक निम्न में से कौन है (A) 6x units (B) 8x units (C)7x units (D) 9x units (v) 1 If it costs Rupees 25/- per square meter to paint the wall then the algebraic expression for the cost of painting the given wall is- दीवाल के पेंटिंग का मूल्य २५ रुपये प्रति वर्ग मीटर हो तो दीवाल के पेंटिंग के मूल्य कितना होगा? (A) 250x (2x+D (B) 250x10 (C) 125x(x+D (D) 500x1-250​

Answer 1

Step-by-step explanation:

दिवार के क्षेत्रफल का बीजगणितीय व्यंजक होगा

Answer 2

• (i) 5(10x + 2 - x²) units² .
• (ii) 3x² units² .
• (iii) 2(5x + 11) units .
• (iv) 6x units .
• (v) Rs. 125(10x + 2 - x²) .

Given :- Refer to image .

To Find :-

(i) What is the algebraic expression for the area of the wall to be painted ?

(ii) The expression for the area of door ?

(iii) The expression represents the perimeter of the wall ?

(iv) The expression represents the perimeter of the window ?

(v) If it costs Rupees 25/- per square meter to paint the wall then the algebraic expression for the cost of painting the given wall is ?

Formula used :-

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

Solution :-

Wall :-

→ Length = (5x + 1) units

→ Breadth = 10 units

So,

→ Area of wall = Length × Breadth = (5x + 1) × 10 = 10(5x + 1) units² ---------- Equation (1)

and,

→ Perimeter of wall = 2(Length + Breadth)

→ Perimeter of wall = 2(5x + 1 + 10)

→ Perimeter of wall = 2(5x + 11) units (Ans.iii)

Door :-

→ Length = x units

→ Breadth = 3x units

So,

→ Area of wall = Length × Breadth = x × 3x = 3x² units² ---------- Equation (2) (Ans.ii)

Window :-

→ Length = 2x units

→ Breadth = x units

So,

→ Area of wall = Length × Breadth = 2x × x = 2x² units² ---------- Equation (3)

and,

→ Perimeter of Window = 2(Length + Breadth)

→ Perimeter of Window = 2(2x + x)

→ Perimeter of Window = 2 × 3x

→ Perimeter of Window = 6x units (Ans.iv)

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) units² . (Ans.i)

therefore,

→ Rate of cost = Rs. 25/m²

hence,

→ Total cost of painting the given wall = Total area to be painted × Rate = 5(10x + 2 - x²) × 25 = Rs. 125(10x + 2 - x²) (Ans.v)

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