Question

If the perimeter and length of a rectangle is 6:1 and the area of the rectangle is 288 cm^2 . Then find the length?​

Answer 1

12 cm(= x) {read the last passage}

Step-by-step explanation:

Let the perimeter and length be 6x and 1x, and, breadth be y. Using:

Perimeter = 2(length + breadth)

=> 6x = 2(x + y)

=> 6x = 2x + 2y

=> 4x = 2y

=> 2x = y

Area of rectangle = length x breadth

=> 288 = x × y

=> 288 = x × (2x)

=> 288 = 2x²

=> 144 = x²

=> 12 = x

Thus, length = x = 12 cm

In this question, length(x) is smaller than breadth(2x) which is not possible. If the question is correct, the bigger one(2x) should be the length abd smaller one(x) breadth. Therefore, 2x = 2(12) = 24 cm is the actual length. Else, your question is incorrect.

Moreover, x = 12 cm.

Answer 2

Given :-

If the perimeter and length of a rectangle is 6:1 and the area of the rectangle is 288 cm^2

To Find :-

Length

Solution :-

Let

$\bf Length= l$

$\bf Breadth = b$

Now,

$\sf 6l = 2(l+b)$

$\sf 6l = 2l + 2b$

$\sf 6l-2l = 2b$

$\sf 4l=2b$

$\sf \dfrac{4l}{2} = \dfrac{2b}{2}$

$\sf 2l =b$

Now,

Area = l × b

288 = l × 2l

288 = 2l²

288/2 = l²

144 = l²

12 = l

So,

Length = 12 cm