Question

The perimeter of a rectangle is 94 cm and its area is 246 cm2. Find the dimensions of the
rectangle.

Answer 1

the perimeter of rectangle = 94

2(l + b )=94

l+b =47

l =47-b . . . . . (1)

the area of the rectangle = 246

lxb =246

(47-b)b=246

b2-47b+246=0

breadth b=6 units

l=47-6

length l =41 units

Answer 2

Answer:

The length of the rectangle is 41 cm and its breadth is 6 cm.

Step-by-step explanation:

We know that the formula for calculating the perimeter of a rectangle is:

$2 \times (l +b)$

The formula for calculating the area of a rectangle is:

$l \times b$

where,

• $l$ is the length of the rectangle.
• $b$ is the breadth of the rectangle.

It has been given that the perimeter of the rectangle is $94 \ cm$.

Therefore, $2 \times (l +b) = 94$

$l +b = \frac{94}{2}$

$l +b = 47$

$l = 47 - b$ ..... (1)

The area of the rectangle is $246 \ cm^{2}$

Therefore, $l \times b = 246$

$l = \frac{246}{b}$........ (2)

Equate (1) and (2)

$47-b = \frac{246}{b}$

$b^{2} -47b+246 =0$

The value of $b$ will come out to be $6$.

Now let us put this value in the first equation to find $l$.

$l = 47 - 6\\l = 41$

Final Answer:

Hence, the length of the rectangle is 41 cm and its breadth is 6 cm.

Link:

https://brainly.in/question/6193599?referrer=searchResults

#SPJ2