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

Given :-

Area of square = 1767m²

Length of rectangle = ⅓ of side of square

Breadth of rectangle = Length of rectangle - 4m

$\begin{gathered}\\\end{gathered}$

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

Area of square - Area of rectangle = ?

$\begin{gathered}\\\end{gathered}$

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

Area of square = Side²

Area of rectangle = Length × Breadth

$\begin{gathered}\\\end{gathered}$

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

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

$\begin{gathered}\\\end{gathered}$

According to the Question :-

Area of square = 1767m²

⇒ Side² = 1767m²

⇒ a² = 1767

⇒ a = √1767

⇒ a ≈ 42

$\begin{gathered}\\\end{gathered}$

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

$\begin{gathered}\\\end{gathered}$

We are given that

Length of rectangle = ⅓ of side of square

⇒ Length of rectangle = $\dfrac{1}{3}31 × 42m$

⇒ Length of rectangle = 14m

∴ Length of rectangle = 14m

$\begin{gathered}\\\end{gathered}$

We are given that :-

Breadth of rectangle = Length of rectangle - 4m

⇒ Breadth of rectangle = 14m - 4m

⇒ Breadth of rectangle = 10m

∴ Breadth of rectangle = 10m

$\begin{gathered}\\\end{gathered}$

We know that :-

Area of rectangle = Length × Breadth

⇒ Area of rectangle = 14m × 10m

⇒ Area of rectangle = 140m²

∴ Area of rectangle = 140m²

$\begin{gathered}\\\end{gathered}$

$\begin{gathered}\\\end{gathered}$

Now we find :-

Area of square - Area of rectangle

⇒ 1767m² - 140m²

⇒ 1627m²

$\begin{gathered}\\\end{gathered}$

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