Answer :
Given :
[tex]\begin{lgathered}\bullet\:\:\textsf{Perimeter of reactangle = \textbf{32 cm}}\\\bullet\:\:\textsf{Width = \textbf{7 cm}}\end{lgathered}[/tex]
[tex]\rule{130}1[/tex]
Solution :
[tex]:\implies\sf Perimeter\:of\: rectangle = 2 (Length + Breadth) \\\\\\:\implies\sf 32 = 2 (l + 7)\\\\\\:\implies\sf 32 = 2l + 14\\\\\\:\implies\sf 32 - 14 = 2l\\\\\\:\implies\sf 2l = 18\\\\\\:\implies\underline{\boxed{\sf Length = 9\:cm}} [/tex]
[tex]\rule{170}2[/tex]
[tex]\dashrightarrow\sf\:\:Area\:of\: rectangle = Length \times Breadth\\\\\\\dashrightarrow\sf\:\: Area\:of\: rectangle = 7\:cm \times 9\:cm\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Area\:of\: rectangle = 63\:cm^2}}[/tex]
⠀
[tex]\therefore\:\underline{\textsf{The area of reactangle is \textbf{63}}\:\sf{cm^2}}.[/tex]
Answer:
Area of the rectangle is 63 cm².
Step-by-step explanation:
Given :-
- The perimeter of a rectangle is 32 cm.
- The width is 7 cm.
To find :-
- The area of the rectangle.
Solution :-
Consider,
- Length of the rectangle = x cm
width = 7 cm
Formula used :-
[tex]{\boxed{\sf{Perimeter of rectangle=2(Length+breadth)}}}[/tex]
According to the question ,
2(x+7) = 32
→ x+7 = 32/2
→ x +7 = 16
→ x = 16-7
→ x = 9
★ Length = 9 cm
Area of the rectangle ,
= length × Breadth
= 9 × 7 cm²
= 63 cm²
Therefore, the area of the rectangle is 63 cm².