Question

the length of the rectangle is 4 times its width. if the perimeter of the rectangle is 80 m.Find the length and breadth of rectangle.​

Answer 1

✬ Length = 32 m ✬

✬ Breadth = 8 m ✬

Step-by-step explanation:

Given:

• The length of a rectangle is 4 times it's width.
• Perimeter of rectangle is 80 m.

To Find:

• What is the measure of length and breadth of rectangle ?

Solution: Let the width of rectangle be x m.

∴ Length = 4 times of x = 4x

★Perimeter of rectangle = 2(Length + Breadth)★

$\implies{\rm }$ 2 ( 4x + x ) = 80

$\implies{\rm }$ 2 ( 5x ) = 80

$\implies{\rm }$ 10x = 80

$\implies{\rm }$ x = 80/10

$\implies{\rm }$ x = 8

Hence, The width of rectangle is 8 m and

Length of rectangle is 4x = 4(8) = 32 m

_______________________

★ ChEck ★

➼ 2 ( 4x + x ) m = 80 m

➼ 2 ( 32 + 8 ) m = 80 m

➼ 2 (40) m = 80 m

➼ 80 m = 80 m { LHS = RHS }

Answer 2

$\huge{\boxed{\overline{\mathrm{\blue{GIVEN:-}}}}}$

• The length of the rectangle is 4 times the breadth
• Perimeter of rectangle is 80 m.

$\huge{\boxed{\overline{\mathrm{\blue{TO\:FIND:-}}}}}$

Find the Length and breadth of the rectangle = ?

$\huge{\boxed{\overline{\mathrm{\blue{FORMULA \:USED:-}}}}}$

$\large{\boxed{\underline{\overline{\mathrm{\green{Perimeter \: rectangle = 2( l + b)}}}}}}$

$\huge{\boxed{\overline{\mathrm{\blue{SOLUTION:-}}}}}$

Let the Length of rectangle be 'l' m and breadth be 'b' m

If the length of the rectangle is 4 times its width.

According to given Conditions :-

$\implies$ $\large\rm\red{ l = 4b....1)}$

The perimeter of rectangle is 80 m

Putting the values in the formula, we get

$\implies$ $\rm{80 = 2(l + b)}$

Put the value of 'l' from equation 1)

$\implies$ $\rm{80 = 2(4b + b)}$

$\implies$ $\rm{80 = 2\times 5b}$

$\implies$ $\rm{80 = 10b}$

$\implies$ $\rm{ b = \cancel\dfrac{80}{10}}$

$\implies$ $\large\bf\red{ b = 8\: m}$

To find the length of the rectangle, put the value of 'b' in equation 1)

$\implies$ $\rm{ l = 4b}$

$\implies$ $\rm{ l = 4\times 8}$

$\implies$ $\large\bf\red{ l = 32 \: m}$

Thus, the length of the rectangle is 32 m and breadth is 8 m

$\large{\boxed{\overline{\mathrm{\blue{FINAL\:ANSWER:-}}}}}$

$\large{\boxed{\boxed{\bf{\red{Length = 32\: m}}}}}$

$\large{\boxed{\boxed{\bf{\red{Breadth = 8 \: m}}}}}$

$\huge{\boxed{\overline{\mathrm{\blue{VERIFICATION:-}}}}}$

Put the values of 'l' and 'b' in the formula

$\large\bf{ perimeter = 2(l+b)}$

$\implies$ $\bf{80 = 2(32 + 8)}$

$\implies$ $\bf{80 = 2(40)}$

$\bf{80 = 80}$

$\implies$ $\bf{[L.H.S. = R.H.S.]}$

$\large{\underline{\underline{\rm{\red{Verified...}}}}}$