Question

[ 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 1

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)

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✩ DIAGRAM:

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

$\rule{150}{2}$

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

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

Answer 2

Solution :

$\underline{\bf{Given\::}}}$

• Two adjacent sides of rectangle = (5x + 6) cm & (2x + 66) cm.
• Perimeter = 186 cm

$\underline{\bf{Explanation\::}}}$

As we know that formula of the perimeter of rectangle :

$\boxed{\bf{Perimeter=2(length+breadth)}}}}}$

A/q

$\longrightarrow\sf{186 = 2[(5x+6)+(2x+66)]}\\\\\longrightarrow\sf{186 = 2(5x+6 + 2x + 66)}\\\\\longrightarrow\sf{186 = 2(7x + 72)}\\\\\longrightarrow\sf{186=14x+144}\\\\\longrightarrow\sf{14x=186 -144}\\\\\longrightarrow\sf{14x = 42}\\\\\longrightarrow\sf{x=\cancel{42/14}}\\\\\longrightarrow\bf{x=3\:cm}$

D I M E N S I O N S :

Length of rectangle = 5x + 6 = 5(3) + 6 = 15 + 6 = 21 cm.

Breadth of rectangle = 2x + 66 = 2(3) + 66 = 6 + 66 = 72 cm

Now;

$\boxed{\bf{Area \:of\:rectangle =length\times breadth\:\:\:(sq.unit)}}}}}$

$\longrightarrow\sf{Area=Length \times breadth}\\\\\longrightarrow\sf{Area=21 cm\times 72 cm}\\\\\longrightarrow\bf{Area = 1512\:cm^{2}}$

Thus;

The area of rectangle will be 1512 cm² .