Question

length of a rectangle is 16cm less than twice it's breadth. if the perimeter of the rectangle is 100cm, find it's length and breadth.

Answer 1

${\red{\underline{\underline{\large{\mathtt{Question:-}}}}}}$

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

${\red{\underline{\underline{\large{\mathtt{To\:find:-}}}}}}$

• Length and breadth of a Rectangle

${\red{\underline{\underline{\large{\mathtt{Answer:-}}}}}}$

Let the breadth be $\bold\red{x}$

And the length be $\bold\red{2x-16}$

So, the perimeter would be

$\implies2(l + b) \\ \implies2(x + 2x - 16) \\ \implies2(3x - 16) \\ \implies6x - 32$

$\underline\green{\star{\:\textsf{Equation:-}}}$

$\implies6x - 32 = 100 \\ \implies6x = 100 + 32 \\ \implies 6x = 132 \\ \implies \: x = \cancel \frac{132}{6}$

$\bold\green{x=22}$

$\mathtt{Breadth\:will\:be\:22cm}$

And Length:-

$\text{2x-16}$

$\text{2(22)-16}$

$\text{44-16}$

$\text{28cm}$

$\therefore{Length=28cm\:and\: Breadth=22cm}$

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Answer 2

Answer:

Length = 28cm

Breadth = 22 cm

Step-by-step explanation:

Let the breadth of rectangle be = x

Length be = 2x - 16

So now, according to the question

= 2(l + b) = 100

= 2(2x - 16 + x) = 100

= 3x = 50 + 16 = 66

= x = 66 ÷ 3

= x = 22 cm

• So, our breadth is 22 cm

So, now the length

= 2x - 16

= 2 × 22 - 16

= 28 cm