Question

The perimeter of a rectangle is 91cm. Its length is (2x-1) cm and breadth is (x+9)cm. Find its length and breadth.
Only correct answers. ​

Answer 1

Given :-

Perimeter of a rectangle = 91 cm

Length of a rectangle = (2x-1) cm

Breadth of a rectangle = (x+9) cm

To Find :-

The length of the rectangle.

The breadth of the rectangle.

Analysis :-

Substitute the length and breadth in the formula of perimeter of a rectangle and make an equation accordingly.

Solve the equation in order to find the value of x

Substitute the value of x in the length and breadth to get their values.

Solution :-

We know that,

• l = Length
• b = Breadth
• p = Perimeter

Given that,

Perimeter (p) = 91 cm

Length (l) = (2x-1) cm

Breadth (b) = (x+9) cm

According to the question,

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

Substituting their values, we get

Perimeter = $\sf 2((2x-1)+(x+9))=91$

= $\sf 2(3x + 8)$

$=\sf 6x + 16=91$

$= \sf 6x=91 - 16$

$=\sf 6x=75$

$= \sf x=\dfrac{75}{6}$

$\sf =x = 12.5 \ cm$

Therefore, the value of x is 12.5 cm

$\sf Length=(2x-1)$

$\sf =((2 \times12.5)-1)=((25)-1)=24 \ cm$

$\sf Breadth=(x+9)$

$\sf =12.5+9=21.5 \ cm$

Therefore, the length and breadth are 24 cm and 21.5 cm respectively.

Answer 2

Step-by-step explanation:

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