[ HUNDRED POINTS]Two adjacent sides of rectangle are 5 x+6 and 2 x + 6

1.	[ HUNDRED POINTS]Two adjacent sides of rectangle are 5 x+6 and 2 x + 66. Find its area if its perimeter is 186 cm.
Answer» GIVEN: Two adjacent sides of RECTANGLE are 5 x+6 and 2 x + 66. Perimeter of Rectangle = 186 cm To find: Area of Rectangle SoluTion: ${\underline{\bf{\bigstar\; Let's\;head\;to\;the\;quesTion\;now,}}}$ Let the length of Rectangle : (5x + 6) Let the Breadth of Rectangle : (2x + 66) ⠀⠀⠀⠀⠀⠀⠀ ✩ DIAGRAM: $\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.5,2){\sf{\large{5x + 6}}}\put(7.7,1){\large\sf{B}}\put(9.3,0.7){\sf{\large{2x + 66}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$ $\rule{150}{2}$ $\underline{\bigstar\:\boldsymbol{According\:to\:Question\::}}\\\\ \sf Perimeter\;of\; Rectangle = 186\;cm\\\\ \maltese\;{\boxed{\sf{Perimeter\;of\; Rectangle\;:\;2(l + b)}}}\\\\ \sf Therefore,\\\\ :\implies\sf 2[(5x + 6) + (2x + 66)] = 186\\\\ :\implies\sf 2(7x + 72) = 186\\\\ :\implies\sf 7x + 72 = \cancel{ \dfrac{186}{2}}\\\\ :\implies\sf 7x + 72 = 93\\\\ :\implies\sf 7x = 93 - 72\\\\ :\implies\sf 7x = 21\\\\ :\implies\sf x = \cancel{ \dfrac{21}{7}}\\\\ :\implies{\underline{\boxed{\sf{\pink{x = 3\;cm}}}}}\;\bigstar$ ${\underline{\bf{\bigstar\;So,\;the\; dimensions\;of\; Rectangle\;are\;:}}}\\\\ \;\;\;\bullet\;\;\sf Length\;of\; Rectangle\;:\;(5x + 6) = 5 \times 3 + 6 = 15 + 6 = \bf{21\;cm}\\\\ \;\;\;\bullet\;\;\sf Breadth\;of\; Rectangle\;:\;(2x + 66) = 2 \times 3 + 66 = 6 + 66 = \bf{72\;cm}\\\\ \therefore\;\sf \underline{Hence,\; Length\;and\; Breadth\;of\; Rectangle\;are\;21\;cm\;and\;72\;cm\; respectively.}$

[ HUNDRED POINTS]Two adjacent sides of rectangle are 5 x+6 and 2 x + 66. Find its area if its perimeter is 186 cm.

Answer»

GIVEN:

Two adjacent sides of RECTANGLE are 5 x+6 and 2 x + 66.

Perimeter of Rectangle = 186 cm

To find:

Area of Rectangle

SoluTion:

${\underline{\bf{\bigstar\; Let's\;head\;to\;the\;quesTion\;now,}}}$

Let the length of Rectangle : (5x + 6)

Let the Breadth of Rectangle : (2x + 66)

⠀⠀⠀⠀⠀⠀⠀

✩ DIAGRAM:

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.5,2){\sf{\large{5x + 6}}}\put(7.7,1){\large\sf{B}}\put(9.3,0.7){\sf{\large{2x + 66}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

$\rule{150}{2}$

$\underline{\bigstar\:\boldsymbol{According\:to\:Question\::}}\\\\ \sf Perimeter\;of\; Rectangle = 186\;cm\\\\ \maltese\;{\boxed{\sf{Perimeter\;of\; Rectangle\;:\;2(l + b)}}}\\\\ \sf Therefore,\\\\ :\implies\sf 2[(5x + 6) + (2x + 66)] = 186\\\\ :\implies\sf 2(7x + 72) = 186\\\\ :\implies\sf 7x + 72 = \cancel{ \dfrac{186}{2}}\\\\ :\implies\sf 7x + 72 = 93\\\\ :\implies\sf 7x = 93 - 72\\\\ :\implies\sf 7x = 21\\\\ :\implies\sf x = \cancel{ \dfrac{21}{7}}\\\\ :\implies{\underline{\boxed{\sf{\pink{x = 3\;cm}}}}}\;\bigstar$

${\underline{\bf{\bigstar\;So,\;the\; dimensions\;of\; Rectangle\;are\;:}}}\\\\ \;\;\;\bullet\;\;\sf Length\;of\; Rectangle\;:\;(5x + 6) = 5 \times 3 + 6 = 15 + 6 = \bf{21\;cm}\\\\ \;\;\;\bullet\;\;\sf Breadth\;of\; Rectangle\;:\;(2x + 66) = 2 \times 3 + 66 = 6 + 66 = \bf{72\;cm}\\\\ \therefore\;\sf \underline{Hence,\; Length\;and\; Breadth\;of\; Rectangle\;are\;21\;cm\;and\;72\;cm\; respectively.}$