Question

Activity 6
The length of a rectangle is 5 metres less than twice the breadth. If the perimeter is 50
metres, find the length and breadth of the rectangle.​

Answer 1

Answer :-

• Length of the rectangle = 15 m.
• Breadth of the rectangle = 10 m.

To find :-

• The length and breadth of the rectangle.

Solution :-

Let the breadth of the rectangle be "x" m.

Then :-

• Twice the breadth will be "2x" m.

5 metres less than twice the breadth will be :-

• "2x - 5" m.

It is given that :-

• The length of the rectangle is 5 metres less than twice the breadth.

Hence :-

• The length of the rectangle is "2x - 5" m.

We know that :-

$\underline{ \boxed{ \sf Perimeter \: of \: a \: rectangle = 2 \: (L + B)}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Perimeter = 50 m.
• Length = "2x - 5" m.
• Breadth = "x" m.

Substituting the given values in this formula,

$\longmapsto\bf50 = 2 \: (x + 2x - 5)$

$\bf\longmapsto 50 =2 \: (3x - 5)$

$\bf\longmapsto 50 = 6x - 10$

$\bf \longmapsto 50 + 10 = 6x$

$\bf \longmapsto 60 = 6x$

$\bf \longmapsto \dfrac{60}{6} = x$

$\longmapsto \overline{ \boxed{ \bf10 \: m = x}}$

-----------------------------------------------------------

Hence, the dimensions of the rectangle are as follows :-

$\sf Length = 2x - 5 = 2 \times 10 - 5 = 15 \: m.$

$\sf Breadth = x = 10 \: m.$

Answer 2

Step-by-step explanation:

let the breadth of rectangle be x

then, the length is 2x-5

we have, perimeter of rectangle=50m

2(x+2x-5)=50

6x=60

x=6

hence the length and breadth is equal to 10and 15 respectively.