Question

the length of a rectangle is 3cm longer than twice the width. if the area if the rectangle is 65 cm^2, find its length and the width

Answer 1

$\textbf{Given:}$

$\textsf{Length of a rectangle is 3cm longer than twice the width and}$

$\textsf{area of the rectangle is 65 square cm}$

$\textbf{To find:}$

$\textsf{Length and breadth}$

$\textbf{Solution:}$

$\textsf{Let l and b be the length and breadth of the given rectangle}$

$\textsf{respectively}$

$\textsf{As per given data,}$

$\mathsf{l=2b+3}$

$\mathsf{Area\;of\;the\;rectangle=65\;cm^2}$

$\implies\mathsf{l{\times}b=65}$

$\implies\mathsf{(2b+3)b=65}$

$\implies\mathsf{2b^2+3b-65=0}$

$\implies\mathsf{2b^2+13b-10b-65=0}$

$\implies\mathsf{b(2b+13)-5(2b+13)=0}$

$\implies\mathsf{(b-5)(2b+13)=0}$

$\implies\mathsf{b=5,\frac{-13}{2}}$

$\textsf{But b cannot be negative}$

$\implies\mathsf{b=5}$

$\textsf{when b=5, l=2(5)+3=13}$

$\textbf{Answer:}$

$\textsf{Length and breadth of the rectangle are 13 cm and 5 cm}$

$\textbf{Find more:}$

The area of a rectangle is 120m^2. If its length is decreased by 8m and its width is increased by 4m, the area stays the same. Find the perimeter of the original rectangle if all measurements are whole numbers, and show your working. Please answer, much appreciated.

https://brainly.in/question/20250117