Question

the length and width of a rectangle are (2x-3y+1) and (5x-4y+2) units . find the perimeter.​

Answer 1

Answer:

14x-14y+21

Step-by-step explanation:

the formula for perimeter of rectangle is 2(lxw)

here l=2x-3y+1

w=5x-4y+2

=2(2x-3y+1+5x-4y+2)

=2(7x-7y+3)

=14x-14y+21

Answer 2

${\large{\pmb{\sf{\underline{Understanding \: the \: Question...}}}}}$

★ This question says that we have to find out the perimeter of a rectangle whose length and breadth is given as (2x-3y+1) unit's and (5x-4y+2) unit's respectively. The diagrams related to this question are given below:

Common diagram for a rectangle without diagonals -

$\begin{gathered} \sf Length \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf Width \end{gathered}$

Diagram for the given rectangle -

$\begin{gathered} \sf (2x-3y+1) \: unit's \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf (5x-4y+2) \: unit's \end{gathered}$

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

★ Length of rectangle = (2x-3y+1) units

★ Breadth of rectangle = (5x-4y+2) units

${\large{\pmb{\sf{\underline{To \; find...}}}}}$

★ Perimeter of the rectangle

${\large{\pmb{\sf{\underline{Solution...}}}}}$

★ Perimeter of the rectangle = 14x - 14y + 6

${\large{\pmb{\sf{\underline{Using \; concept...}}}}}$

★ Formula to find out the perimeter of the rectangle.

${\large{\pmb{\sf{\underline{Using \; Formula...}}}}}$

${\small{\underline{\boxed{\sf{\bigstar \: Perimeter \: = 2(l+b)}}}}}$

${\large{\pmb{\sf{\underline{Full \; Solution...}}}}}$

${\small {\underline {\boxed {\sf Perimeter \: = 2(l+b)}}}} \\ \\ :\implies \sf Perimeter \: = 2(l+b) \\ \\ :\implies \sf Perimeter \: = 2[2x-3y+1 + (5x-4y+2)] \\ \\ :\implies \sf Perimeter \: = 2[2x-3y+1 + 5x - 4y + 2] \\ \\ :\implies \sf Perimeter \: = 2(2x + 5x - 3y - 4y + 1 + 2) \\ \\ :\implies \sf Perimeter \: = 2(7x - 7y + 3) \\ \\ :\implies \sf Perimeter \: = 14x - 14y + 6 \: unit$