Question

The area of a square is 1767 m2 (approx.) and length
of rectangle is one-third of side of that square. If
breadth of rectangle is 4m less than length of
rectangle, then find difference between area of square
and area of rectangle.
(a) 1609 m2 (b) 1627 m2 (C) 1664 m2
(d) 1729 m2 (e) 1709 m2
​

Answer 1

Answer:

• Option (b) 1627 m²

Steps:

Let the length of the side of the square be 'a' units.

Hence using the formula of calculating area for a square we get:

→ Area of Square = (Side)²

→ Area of the Square = (a)²    ...(i)

According to question, area of the square is 1767 m² (approx). Using it in (i) we get:

→ a² = 1767 (approx)

→ a = √1767

⇒ a = 42 m (approx.)

Now it is given that, the length of rectangle is one-third of the side of the square. Hence length of the rectangle is:

→ Length of rectangle = a / 3

→ Length of rectangle = 42 / 3 = 14 m.

Also, the breadth of the rectangle is 4 m less than the length of the rectangle. Hence,

→ Breadth of the rectangle = Length - 4

→ Breadth = 14 - 4 = 10 m.

Hence Area of the rectangle is calculated as:

→ Area of rectangle = Length × Breadth

→ Area of rectangle = 14 m × 10 m

⇒ Area of rectangle = 140 m²

Hence the difference in Area of Square and Area of rectangle is:

⇒ Area of Square - Area of Rectangle

⇒ 1767 m² - 140 m²

⇒ 1627 m²

Hence the difference in areas is 1627 m².

Hence Option (b) is the right answer.

Answer 2

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Given :-}}}}}}$

☞ Area of square = 1767m²

☞ Length of rectangle = ⅓ of side of square

☞ Breadth of rectangle = Length of rectangle - 4m

$\Large{\underline{\underline{\textsf{\maltese\: {\red{To Find :-}}}}}}$

☞ Area of square - Area of rectangle = ?

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Recapitulating the concepts :-}}}}}}$

☞ Area of square = Side²

☞ Area of rectangle = Length × Breadth

$\Large{\underline{\underline{\textsf{\maltese\: {\red{Solution :-}}}}}}$

Let the length of side of square be ‘a’ metres.

According to the Question,

Area of square = 1767m²

⇒ Side² = 1767m²

⇒ a² = 1767

⇒ a = √1767

⇒ a ≈ 42

∴ The length of side of square is 42m approximately.

We are given that

☞ Length of rectangle = ⅓ of side of square

⇒ Length of rectangle = $\frac{1}{3}$ × 42m

⇒ Length of rectangle = 14m

∴ Length of rectangle = 14m

We are given that

☞ Breadth of rectangle = Length of rectangle - 4m

⇒ Breadth of rectangle = 14m - 4m

⇒ Breadth of rectangle = 10m

∴ Breadth of rectangle = 10m

We know that

☞ Area of rectangle = Length × Breadth

⇒ Area of rectangle = 14m × 10m

⇒ Area of rectangle = 140m²

∴ Area of rectangle = 140m²

Now we find

Area of square - Area of rectangle

⇒ 1767m² - 140m²

⇒ 1627m²

∴ Area of square - Area of rectangle = 1627m².

Hence Option 【B】✅ is correct. :-)