Question

Solve all 4 Questions . 50 Points + Brainelist ​

Answer 1

Given:

• The length of the rectangular shaped lamina is 5 cm more than the length of the square shaped lamina.
• The breadth of the rectangular shaped lamina is 3 cm less than the length of the square shaped lamina.
• x = side length of square

i) Length of rectangular shaped lamina = (x + 5) cm

ii) Breadth of rectangular shaped lamina = (x - 3) cm

ii) Area of a rectangle = length × breadth

⇒ area of rectangular shaped lamina = (x + 5)(x - 3) cm²

Given:

• area of rectangular shaped lamina = 105 cm²

⇒ (x + 5)(x - 3) = 105

Expand:

⇒ x² - 3x + 5x - 15 = 105

Combine like terms:

⇒ x² + 2x - 15 = 105

Subtract 105 from both sides:

⇒ x² + 2x - 120 = 0

iv) Solve x² + 2x - 120 = 0

Rewrite:

⇒ x² + 12x - 10x - 120 = 0

Break into groups:

⇒ (x² + 12x) - (10x + 120) = 0

Factorize the parentheses:

⇒ x(x + 12) - 10(x + 12) = 0

Factor out common term:

⇒ (x - 10)(x + 12) = 0

Therefore,

x - 10 = 0 ⇒ x = 10

x + 12 = 0 ⇒ x = -12

As length is positive, x = 10 only

Therefore,

Length of rectangular shaped lamina = 15 cm

Breadth of rectangular shaped lamina = 7 cm

Answer 2

Here given:

• length of square : x

i)

• length of rectangle : x + 5

ii)

• breadth of rectangle : x - 3

iii)

• area of rectangle = length * breadth

• 105 = (x + 5)(x - 3)

• 105 = x² + 2x - 15

• x² + 2x - 15 - 105 = 0

• x² + 2x - 15 - 105 = 0

• x² + 2x - 120 = 0

iv)

• x² + 2x - 120 = 0

• x² + 12x -10x - 120 = 0

• x( x + 12) -10 (x +12) = 0

• (x-10)(x+12)

• x = 10, -12

With x = -12, Not applicable so x will be 10

Length → x + 5 → 10 + 5 → 15

Breath → x -3 → 10 - 3 → 7

Therefore,

Length : 15 cm

Breadth : 7 cm