Question

if the breadth of a rectangle is 2/3rd of its length if the perimeter is 150 them find dimensions of the rectangle​

Answer 1

★ Understanding the question :

» Here we have a rectangle whose breadth(b) is 2/3rd of it's length(l). It's perimeter is 150 units.

» We had to find out the length and width of the given rectangle.

Let's do it !!

ㅤㅤㅤㅤㅤㅤ━━━━━━━━

$\underbrace{\underline{\sf{Required\:solution\::}}}$

• Let length(l) of a rectangle = x units

So,

• Breadth(b) of a rectangle = 2/3 x units

✎ Using formula of perimeter of ㅤㅤㅤㅤrectangle :

$\qquad:\implies\:\sf Perimeter_{(Rectangle)} = 2(l + b)$

★ Values that we have :

• Perimeter = 150 units
• l = x units
• b = 2/3 x units

✎ Putting all values in the formula :

$\qquad:\implies\:\sf 150 = 2(x + \dfrac{2}{3}x)$

$\qquad:\implies\:\sf 150 = 2(\dfrac{3x + 2x}{3})$

$\qquad:\implies\:\sf 150 = 2(\dfrac{5}{3}x)$

$\qquad:\implies\:\sf 150 = \dfrac{10}{3}x$

$\qquad:\implies\:\sf 150\:\times\:3 = 10x$

$\qquad:\implies\:\sf 450 = 10x$

$\qquad:\implies\:\sf \dfrac{450}{10} = x$

$\qquad:\implies\:\sf \dfrac{45\cancel{0}}{1\cancel{0}} = x$

$\qquad:\implies\:\bold {x = \red{45\:units}}$

Therefore,

➱ Length = x = 45 units

And,

➱ Breadth = 2/3 × x = 2/3 × 45 = 2 × 15 = 30 units

$\small\underline{\boxed{\tt{Length\:and\:Breadth\:of\:rectangle\:=\:\rm\purple{45\:units}\:\tt{and}\:\rm\purple{30\:units}}}}$

This is the required answer.

Answer 2

Answer:

★ Understanding the question :

» Here we have a rectangle whose breadth(b) is 2/3rd of it's length(l). It's perimeter is 150 units.

» We had to find out the length and width of the given rectangle.

Let's do it !!

ㅤㅤㅤㅤㅤㅤ━━━━━━━━━

$\red{\underbrace{\underline{\sf{Required\:solution\::}}}}$

• Let length(l) of a rectangle = x units

So,

• So,Breadth(b) of a rectangle = 2/3 x units

✎ Using formula of perimeter of ㅤㅤㅤㅤrectangle :

$\pink{\odot} \purple{\ \: \:\sf Perimeter_{(Rectangle)} = 2(l + b):}$

★ Values that we have :

• Perimeter = 150 units
• Perimeter = 150 unitsl = x units
• Perimeter = 150 unitsl = x unitsb = 2/3 x units

✎ Putting all values in the formula :

$\qquad:\implies\:\sf 150 = 2(x + \dfrac{2}{3}x)$

$\qquad:\implies\:\sf 150 = 2(\dfrac{3x + 2x}{3})$

$\qquad:\implies\:\sf 150 = 2(\dfrac{5}{3}x)$

$\qquad:\implies\:\sf 150 = \dfrac{10}{3}$

$\qquad:\implies\:\sf 150\:\times\:3 = 10x$

$\qquad:\implies\:\sf 450 = 10x:$

$\qquad:\implies\:\sf \dfrac{450}{10} = x$

$\qquad:\implies\:\sf \dfrac{45\cancel{0}}{1\cancel{0}} = x$

$\qquad:\implies\:\bold {x = \red{45\:units}}$

Therefore,

➱ Length = x = 45 units

➱ Length = x = 45 unitsAnd,

➱ Breadth = 2/3 × x = 2/3 × 45 = 2 × 15 = 30 units

$\red{\small\underline{\boxed{\tt{Length\:and\:Breadth\:of\:rectangle}\:=\:\rm\purple{45\:units}\:\tt{and}\:\rm\purple{30\:units}}}}$

This is required Answer:-