Question

a rectangular piece is twice as long as a square piece and 3 cm wide. the area of the rectangular piece is 108 cm^2. find the dimensions of the square piece.

Answer 1

Answer:-

Given:

The length of a rectangular piece is twice the side of a square piece.

Let the side of the square be x cm.

So, Length of the rectangle = 2(x) = 2x cm

Also given that,

Width of the rectangle = 3 cm

Area of the rectangle = 108 cm²

We know that,

Area of a rectangle = length * breadth

According to the question,

⟹ (2x)(3) = 108

⟹ 6x = 108

⟹ x = 108/6

⟹ x = 18 cm

∴ Each side of the square is 18 cm.

Answer 2

Answer:

Given :

• a rectangular piece is twice as long as a square piece and 3 cm wide.

• the area of the rectangular piece is 108 cm^2.

To Find :

• find the dimensions of the square piece

Solution :

Length of rectangle = 2(length of square)

Concept :

• According to the Webster's Ninth Collegiate Dictionary, length means "the longer or longest dimension of an object."

• So the length of a rectangle is the longest side whether it is vertical or horizontal

__________________________

Using the formula :

We can find the area of rectangle by using the formula :

We know that,

• Area of the rectangle = length × breadth

Putting the value in the above formula we can find it area easily.

$: \implies \: \: \: \: \: \boxed{ \sf \: Area \: of \: rectangle = l × \times b }$

Substitute all values :

$: \implies \sf \: \: \: \: \: \: \:108 = 3 \times 2x \\ \\ \\ : \implies \sf \: \: \: \: \: \: \:108 = 6x \\ \\ \\ : \implies \sf \: \: \: \: \: \: \:x = \cancel{\frac{108}{6} } \\ \\ \\ : \implies \sf \: \: \: \: \: \: \:x = 18$

• Therefore, the length of the square is 18 cm