Question

the length of a rectangular field is 15 more than thrice its breadth if the perimeter of a rectangle is 222 cm find the area of field​

Answer 1

$\large\boxed{\mathtt\red{Solution:-}}$

Assumption :-

• Let the Breadth of rectangle be b
• then, the Length of rectangle be 15+3b

Solution :-

→ Perimeter of Rectangle = 222 cm

we know :-

⦿ Perimeter of rectangle = 2[Length+Breadth]

According to the question :-

✒ 222 = 2[15+3b+b]

✒ 222/2 = 15+4b

✒ 111 = 15+4b

✒ 4b = 111-15

✒ b = 96/4

$\small\boxed{\mathtt\green{∴ b=24\:cm}}$

Therefore :-

• Breadth = b = 24 cm
• Length = 15+3b = 15+72 = 87 cm

Now, For Area :-

✒ Area = Length×Breadth

✒ Area = 24 cm × 87 cm

$\small\boxed{\mathtt\red{∴ Area\: of \:Rectangle = 2088 cm²}}$

Answer 2

Given Information :-

The length of a rectangular field is 15 more than thrice its breadth if the perimeter of a rectangle is 222 cm find the area of field ?

• Perimeter of rectangle = 222 cm
• Length of rectangle = 15 + 3b
• Let the breadth of rectangle = b
• Area of field = ?

Using formula,

• Perimeter of rectangle is twice the sum of its length and breadth.
• Mathematical can be written as :

${\dashrightarrow{ \sf{Perimeter = 2 (l+ b)}}}$

Where,

• L = Length of rectangle
• B = Breadth of rectangle

Substituting the given values in the above equation: we get,

→ 222 = 2 ( 15 + 3b + b )

→ 222 = 2 (15 + 4b)

→ 222/2 = 15 + 4b

→ 111 = 15 + 4b

→ 4b = 111 - 15

→ 4b = 96

→ b = 96/4

→ b = 24

Therefore,

• Length of rectangle = 15 + 3b

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 15 + 3 × 24

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 15 + 72

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 87 cm.

• Breadth of rectangle = 24 cm.

Now,

We know that,

Area of rectangle = Length × Breadth

We have,

• Length = 87 cm
• Breadth = 24cm

Substituting the given values in the above equation: we get,

Area of rectangle = 87 × 24

Area of rectangle = 2088 cm².

${\underline{\underline{ \sf{Learn \:More :-}}}}$

$\begin{gathered}\begin{gathered}\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}\end{gathered}\end{gathered}$