Question

Length of a rectangle is 16 cm less than twice its breadth. If the perimeter of the rectangle is 100 cm, find its length and breadth.


PLEASE , IT'S URGENT , ANSWER FAST!!!!!!​

Answer 1

$\Large \pink{ \underline{\textsf{Required Answer }} \downarrow}$

Given:

• Length of a rectangle is 16 cm less than twice its breadth.

• Perimeter of rectangle = 100 cm

To find:

• Length

• Breadth

Let:

• Breadth = x

• Length = 2x - 16

Now we know:

$\bigstar \boxed{ \textrm{Perimeter of rectangle = 2(Length + Breadth)}}$

Using this formula we can find value of x

$\dashrightarrow \textsf{Perimeter of rectangle = 2(Length + Breadth)}$

$\dashrightarrow \textsf{100 = 2(x + 2x - 16)}$

$\dashrightarrow \sf{100= 2(x)+ 2(2x - 16)}$

$\dashrightarrow \sf{100 = 2x+ 2(2x - 16)}$

$\dashrightarrow \sf{100= 2x+ 2 \{2x \} - 2 \{16 \}}$

$\dashrightarrow \sf{100= 2x+ 4x- 2 \{16 \}}$

$\dashrightarrow \sf{100= 2x+ 4x-3 2}$

$\dashrightarrow \sf{100=6x-3 2}$

$\dashrightarrow \sf{100 + 32=6x}$

$\dashrightarrow \sf{132=6x}$

$\dashrightarrow \sf{6x = 132}$

$\dashrightarrow \sf{x = \frac{132}{6} }$

$\dashrightarrow \sf{x = \cancel\frac{132}{6} }$

$\dashrightarrow \sf{x =22}$

$\pink{ \textsf{Verification} \downarrow}$

$\dashrightarrow \sf{100 = 2(x + 2x - 16)}$

$\dashrightarrow \sf{100 = 2(22 + \{ 2 \times 22 \}- 16)}$

$\dashrightarrow \sf{100 = 2(22 + \{ 44 \}- 16)}$

$\dashrightarrow \sf{100 = 2(66- 16)}$

$\dashrightarrow \sf{100 = 2(50)}$

$\dashrightarrow \sf{100 = 2 \times 50}$

$\dashrightarrow \sf{100 =100}$

$\sf \large{} \dag{}LHS = RHS \dag$

$\sf \large{} Hence \: verified$

Finally:

• Breadth = x
• Breadth = 22cm

• Length = 2x - 16
• Length = 2 × 22 - 16
• Length = 44 - 16
• Length = 28cm