Question

the length of the rectangle exceeds the breadth by 6 and diameter if the length is increased by 3 cm and the breadth is decreased by 2 then the area remains the same find the length and the breadth of the rectangle​

Answer 1

Answer:

A/q;

Case 1

let B=x

L=6+x

Area=l*b

       =6x+x^2

Case 2

B=x-2

L=6+3+x=9+x

Area=(x-2)(9+x)

        =9x+x^2-18-2x

        =7x+x^2-18

A/q

6x+x^2=7x+x^2-18

=6x-7x=-18

=-x=-18

Therefore x=18

Hence L=x+6

             =18+6

               =24 cm

B=x=18cm

Step-by-step explanation:

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Answer 2

Answer:

★ Length = 24 cm ★

★ Breadth = 18 cm ★

Step-by-step explanation:

Given:

• Length of rectangle exceeds the breadth by 6 cm
• Length is increased by 3 cm.
• Breadth is decreased by 2 cm.

To Find:

• Length and Breadth of rectangle

Solution: Let the breadth of rectangle be x cm

∴ Its length will be x + 6 cm

★ Area of rectangle= Length x Breadth★

• x + 6 (x) = x² + 6x

A/q , Length is increased by 3 cm and breadth is decreased by 2 cm

∴ New length = x + 6 + 3 cm

• New breadth = x –2 cm

Since, in both cases area remains same therefore,

$\small\implies{\sf }$ x² + 6x = (x + 9) ( x –2)

$\small\implies{\sf }$ x² + 6x = x(x–2) +9(x–2)

$\small\implies{\sf }$ x² + 6x = x² –2x + 9x –18

$\small\implies{\sf }$ x² – x² = –2x –6x + 9x –18

$\small\implies{\sf }$ 18 = –8x + 9x

$\small\implies{\sf }$ 18 = x

Hence, Breadth of rectangle is x = 18 cm

∴ Length of rectangle will be x + 6 = 18 + 6 = 24 cm