Question

Please help with this

Answer 1

Given :-

• Length of rectangular field is 5 1/4 m
• Breadth of rectangular field is 1 1/7 m

To find :-

• Area and Perimeter of a rectangle

Formula Implemented:-

$\bigstar \underline{\boxed{ \sf{{Area}_{(Rectangle)} = Length \times Breadth}}}$

$\bigstar \underline{\boxed{ \sf{{Perimeter}_{(Rectangle)} = 2(Length \times Breadth)}}}$

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SoLuTiOn :-

$5 \dfrac{1}{4} = \dfrac{21}{4}$

$1 \dfrac{1}{7} = \dfrac{8}{7}$

$length \: of \: rectangle = \dfrac{21}{4}$

$breadth \: of \: rectangle \: = \dfrac{8}{7}$

Perimeter = 2(l + b)

$P \: = 2 \bigg(\dfrac{21}{4} + \dfrac{8}{7}\bigg)$

$P \: = 2 \bigg(\dfrac{21\times 7 + 8\times 4}{28}\bigg)$

$P = 2\bigg(\dfrac{147 + 32}{28}\bigg)$

$P =2 \times \bigg( \dfrac{179}{28} \bigg)m$

$P = \dfrac{179}{14} m$

So, Perimeter of recatngle = 179/14 m

Area of recatngle = l × b

$= \dfrac{21}{4} \times \dfrac{8}{7}$

$= 3 \times 2$

$= 6m {}^{2}$

So, Area of rectangle is 6m²

Answer 2

Answer:

Given:-

Length of a rectangular field is $5 \ \frac{1}{4}m$ and breadth is $1 \ \frac{1}{7}m$. Find the area and perimeter of the field.

To Find:-

Area and Perimeter of the rectangular field.

Note:-

●》Area of the rectangular field = Length × Breadth.

●》Perimeter of the rectangular field = 2 × ( Length + Breadth ).

Solution:-

[ First, Area ]

$\huge\red{Length = 5 \ \frac{1}{4}m, Breadth = 1 \ \frac{1}{7}m}$

$\huge\red{Area = ?}$

☆ According to note first point~

▪︎$Area \ \ of \ \ the \ \ rectangular \ \ field = Length × Breadth$

▪︎$Area \ \ of \ \ the \ \ rectangular \ \ field = 5 \ \frac{1}{4}m × 1 \ \frac{1}{7}m$

▪︎$Area \ \ of \ \ the \ \ rectangular \ \ field = \frac{5×4+1}{4}m × \frac{1×7+1}{7}$

▪︎$Area \ \ of \ \ the \ \ rectangular \ \ field = \frac{21}{4}m × \frac{8}{7}m$

☆ m into m = m²~

▪︎$Area \ \ of \ \ the \ \ rectangular \ \ field = \frac{168}{28}m²$

☆ After doing calculations~

▪︎$Area \ \ of \ \ the \ \ rectangular \ \ field = 6m²$

$\huge\green{Area \ \ of \ \ the \ \ rectangular \ \ field = 6m²}$

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[ Now, Perimeter ]

$\huge\red{Length = 5 \ \frac{1}{4}m, Breadth = 1 \ \frac{1}{7}m}$

$\huge\red{Perimeter = ?}$

☆ According to note second point~

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = 2 × ( Length + Breadth )$

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = 2 × ( 5 \ \frac{1}{4}m + 1 \ \frac{1}{7}m )$

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = 2 × ( \frac{5×4+1}{4}m + \frac{1×7+1}{7}m )$

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = 2 × ( \frac{21}{4}m + \frac{8}{7}m )$

☆ Here, we will take L.C.M, L.C.M = 28~

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = 2 × ( \frac{21}{4} × \frac{7}{7} \ \ m + \frac{8}{7} × \frac{4}{4} \ \ m )$

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = 2 × ( \frac{147}{28}m + \frac{32}{28}m )$

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = 2 × \frac{179}{28}m$

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = \frac{358}{28}m$

☆ After making in its lowest term~

▪︎$Perimeter \ \ of \ \ the \ \ rectangular \ \ field = \frac{179}{14}m$

$\huge\green{Perimeter \ \ of \ \ the \ \ rectangular \ \ field = \frac{179}{14}m}$

Answer:-

Hence,

• The Area of the rectangular field = 6m²
• The Perimeter of the rectangular field = $\frac{179}{14}m$.

:)