Question

The length of a rectangle is twice as long as
the side of a square. The side of a square is
4 cm longer than the width of the same
rectangle. If their areas are equal, find their
dimensions.
[4 Marks]​

Answer 1

Answer:

Length of rectangle = 16 cm

Width of rectangle = 4 cm

Side of square = 8 cm

Step-by-step explanation:

Let the width of the rectangle be x cm.

A/q, Side of the square = (x + 4) cm

Also, Length of rectangle = 2(Side of square)

On further solving, we get

→ Length = 2(x + 4)

Now,

A.T.Q.,

Area of square = Area of rectangle

→ (Side of square)² = Length of rectangle × Width of rectangle

Putting the known values, we get

→ (x + 4)² = 2(x + 4) × x

→ x² + 16 + 8x = 2x(x + 4)

→ x² + 16 + 8x = 2x² + 8x

→ 2x² - x² + 8x - 8x - 16 = 0

→ x² - 16 = 0

→ x² = 16

→ x = √16

→ x = ± 4

Dimensions can't be negative.

Hence, x = 4 cm

________________________

• Length of rectangle = 2(x + 4)

→ 2(4 + 4)

→ 2(8)

→ 16 cm

_________________________

• Width of rectangle = x

→ 4 cm

_________________________

• Side of square = (x + 4)

→ (4 + 4)

→ 8 cm

Answer 2

$\huge{\boxed{\boxed{\tt{Answer:}}}}$

Given:

• The length of a rectangle is twice as long as the side of a square.

• The side of a square is 4 cm longer than the width of the same.

rectangle.

Find:

Find their dimensions.

Calculations:

Let y cm be the width of the rectangle.

Let (y + 4) cm be side of the square.

Formula:

$\sf\rightarrow Length \: of \: rectangle = 2 \: (side \times side) . \\ \sf \rightarrow Area \: of \: square = Area \: of \: rectangle. \\ \sf\rightarrow (Side \times side)^{2} = Length \: of \: rectangle \times Width \: of \: rectangle.$

Adding values to the above formulas:

$\sf\rightarrow (y + 4)^2 = 2(y + 4) × y \\ \sf \rightarrow y^2+ 16 + 8y = 2y(y + 4) \\\sf \rightarrow y^2 + 16 + 8y = 2y^2+ 8y \\ \sf \rightarrow 2y^2 - y^2 + 8y - 8y - 16 = 0 \\ \sf \rightarrow y^2 - 16 = 0 \\ \sf \rightarrow y^2 = 16 \\ \sf \rightarrow y = \sqrt{16} \\ \sf\rightarrow y = \pm 4$

Dimensions shouldn't be negative, so the value of y = 4 m.

$\sf\rightarrow 2(x + 4) = Length \: of \: rectangle \\ \sf \rightarrow 2(4 + 4) \\ \sf \rightarrow 2 \times 8 \\ \sf \rightarrow 16 cm$

$\sf \rightarrow y = width \: of \: rectangle \\\sf \rightarrow 4 cm$

$\sf \rightarrow (y+4) = Side \: of \: square \\ \sf \rightarrow (4 + 4) \\ \sf \rightarrow 8 \: cm$