Question

1. The length of a rectangle is 1 cm greater than the breadth. a) If breadth is taken as x, find length?
b) If the perimeter is 50 cm, find length and breadth?

Answer 1

Step-by-step explanation:

Given :-

Length of rectangle = 1 cm + breadth

Breadth = x

Perimeter of the rectangle = 50 cm

To Find :-

Length of the rectangle.

Breadth of the rectangle.

Solution :-

We know that,

l = Length

b = Breadth

h = Height

Let the breadth be x,

Also by given,

Length = 1 + breadth

Length = 1 + x

The perimeter of a rectangle is given by the formula,

\underline{\boxed{\sf Perimeter \ of \ a \ rectangle = 2( Length +breadth) }}

Perimeter of a rectangle=2(Length+breadth)

Where l is the length and b is the breadth of the rectangle,

Substituting their values, we get

\sf 50 = 2 (1 +x +x)50=2(1+x+x)

\sf \dfrac{5}{2} = 2x + 1

2

5

=2x+1

\sf 2x + 1 = 252x+1=25

\sf 2x = 242x=24

\sf x=\dfrac{24}{2}x=

2

24

\sf x = 12x=12

Hence, breadth of the rectangle is 12 cm

Length of the rectangle = \sf 1 +x = 1 + 12 = 13 \ cm1+x=1+12=13 cm

Therefore, the length and breath of the rectangle is 13 cm and 12 cm respectively