Question

the length of rectangle is three times its breadth if the perimeter is 24 find the length of the rectangle​

Answer 1

2×(3x+X)=24

2(4X)=24

8x=24

X=24/8

X=3

3x=3×3=9

X=3

length=9

breadth=3

Answer 2

The Length of Rectangle is three times it's breadth.

The Perimeter of Rectangle is 24 cm.

━━━━━━━━━━━━━━━━━━━━━━━━━━

✇ Let the Breadth of Rectangle be x.

✇ Therefore, Length of Rectangle is 3x.

⋆ Reference of image is shown in diagram

⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀

We know that,

$\star\;{\boxed{\sf{\purple{Perimeter_{\;(Rectangle)} = 2(l + b)}}}}$

Now, Putting values in formula,

$:\implies\sf 2(3x + x) = 24$

$:\implies\sf 2(4x) = 24$

$:\implies\sf 8x = 24$

$:\implies\sf x = \cancel{ \dfrac{24}{8}}$

$:\implies{\boxed{\frak{\pink{x = 3}}}}\;\bigstar$

Therefore,

• Length of Rectangle = 3 × x = 9 cm

• Breadth of Rectangle = x = 3 cm

$\therefore$ Dimensions of Rectangle, Length and Breadth are 9 cm and 3 cm respectively.