Question

13. A rectangle and a square have the same perimeter 100 cm. Find the side of the square. If the rectangle has a breadth 2 cm less than that of the square. Find the breadth, length and area of the rectangle
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Answer 1

Solution :-

Perimeter of square = Perimeter of rectangle

Perimeter of square = 4 × side

4 × side = 100

side = 100/4

Side = 25 cm

Breadth of rectangle = 25 - 2

= 23 cm

Let length of rectangle be L.

Perimeter of rectangle = 2(L + B)

100 = 2(L + 23)

L = 100/2 - 23

L = 50 - 23

L = 27 cm

Area of rectangle = L × B

= 27 × 23

= 621 cm²

Answer 2

Solution:

Perimeter of the square = Perimeter of triangle = 100 cm

Perimeter of the square = 4 × side

$\sf{ \hookrightarrow \: 4 \times side - 100}$

$\sf{ \hookrightarrow \: side = \frac{100}{4} }$

$\sf \pink{ \mapsto \: 25m}$

Let's find Breadth of the triangle :

$\sf{ \hookrightarrow \: 25 - 2}$

$\sf \pink{ \mapsto \: 23m}$

Let the length of the triangle‎‎‎‎‎‎‎‎

$‎‎‎‎‎‎ \sf \purple{ \leadsto \: L \: m}$

Perimeter of rectangle = 2(l + b)

$\sf \orange{ \hookrightarrow \: 100 = 2(l + 23)}$

$\sf \orange{ \hookrightarrow \: l = \frac{100}{2} - 23}$

$\sf \red{ \hookrightarrow \:50 - 23}$

$\sf \pink{ \mapsto \: 27m}$

Area of rectangle = l × b

$\sf \orange{ \hookrightarrow \: 27 \times 23}$

$\sf \pink{ \mapsto \: 621 {m}^{2} }$

Hence,

The breath, length and area of the rectangle is 621 m²

Know more:-

• Perimeter of a square = 4 × side
• Area of square = side × side
• Perimeter of rectangle = 2( l + b )
• Area of rectangle = l × b
• Perimeter of rhombus = 4 × side
• Area of rhombus = ½ × d1 × d2