Question

A rectangle has an area of 24 cm'. If its length is x cm, write down its breadth in terms of x. Given that its perimeter is 20 cm, form an equation in x and solve it.

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Answer 1

Answer:

Length of the rectangle = 12 cms Breadth of the rectangle = 2 cms.

Step-by-step explanation:

Length of rectangle = x cm

Let the breadth of the rectangle be y cm.

Area of rectangle = 24cm

Therefore, Area of rectangle = l x b

24 cm = xy --------- equ. 1

Now, perimeter of rectangle = 20 cm

=2 (l+b)

20 cm= 2 (x+y)

2x + 2y = 20 --------equ. 2

From equ. 2:

2y = 20 - 2x

$\frac{20 - 2x}{2} = y$

From equ. 1:

$\frac{24}{x} = y \:$

From above equations:

$\frac{20 - 2x}{2} = \frac{24}{x}$

$20x - {2x}^{2} = 48$

$- 2x^{2} + 20x - 48 = 0$

$2 {x}^{2} - 20x + 48 = 0$

$2 {x}^{2} - 24x + 4x - 48 = 0$

$2x(x - 12) + 4(x - 12) = 0$

$(2x + 4)(x - 12) = 0$

$2x + 4 = 0 \: and \: x - 12 = 0$

$2x + 4 = 0$

$x = - 2$

And,

$x - 12 = 0$

$x = 12$

Now, since. measurement cannot be negative.

Therefore,

$x = 12$

Substitute x = 12 in equ. 1:

Therefore,

$xy = 24$

$12y = 24$

$y = 2$

Therefore, the length of the rectangle is 12 cms and the breadth of the rectangle is 2 cms.

Regards,

Arnav.

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Answer 2

Answer:

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