Question

The length and width of a rectangle are ( 2x -5) and ( 3 x +4) What is the Perimeter?

Answer 1

Answer:

$\fbox{ \sf{Perimeter \: of \: a \: rectangle = 10x - 2}}$

Step-by-step explanation:

$\star{ \sf{ \: \: Length \: of \: a \: rectangle ( l ) = (2x - 5) }}$

$\star{ \sf{ \: Width \: of \: a \: rectangle ( w ) = (3x + 4)}}$

$\star{ \sf{ \: \: Perimeter \: of \: a \: rectangle = ?}}$

$\boxed{ \bold{ \sf{Perimeter \: of \: a \: rectangle = 2(l + w)}}}$

$\hookrightarrow{ \sf{Perimeter \: of \: a \: rectangle = 2(2x - 5 + 3x + 4)}}$

$\text{Step \: 1 : \: Collect \: like \: term}$

$\text{Like \: terms \: are \: those \: which \: have \: the \: same \: base}$

$\hookrightarrow{ \sf{2(2x + 3x - 5 + 4)}}$

$\hookrightarrow{ \sf{2(5x - 5 + 4)}}$

$\text{Step \: 2 \: : \: Subtract \: 4 \: from \: 5}$

$\text{Remember !\: : the \: negative \: and \: positive \: integers \: are \: always \: subtracted \: but \: posses \: the \: sign \: of \: the \: bigger \: integer}$

$\hookrightarrow{ \sf{2(5x - 1)}}$

$\text{Step \: 3 \: : \: Distribute \: 2 \: through \: the \: parentheses}$

$\hookrightarrow{ \sf{2 \times 5x - 2 \times 1}}$

$\hookrightarrow{ \sf{10x - 2}}$

$\sf{∴ \: The \: perimeter \: of \: a \: rectangle = 10x - 2}$

$\text{Hope \: I \: helped !}$

$\text{Best \: regards ! }$

~$\text{TheAnimeGirl}$