Question

The ratio of the areas of a rectangle to a square is 8:9. If the perimeter of each of them is 48cm, then find the dimensions of the rectangle. please give a detailed and quick answer!! please solve on a paper it's a humble request

Answer 1

Dimensions of the square:

 For a square of side x, perimeter = 4x


4x = 48

x = 12 cm


Area of square = 12x12 = 144


The ratio of the areas of a rectangle to a square is 8:9.


Area of rectangle: Area of square = 8:9


Area of rectangle:144 = 8:9

Area of rectangle/144 = 8/9

Area of rectangle = 144(8/9) = 128 cm^2

If the rectangle has dimensions of a, b

Area = ab = 128 -------- (i)

Perimeter = 2(a + b) = 48

a + b = 24 -------- (ii)

From (i), b = 128/a


Substitute in (ii)

a + b = 24

a + 128/a = 24

a^2 – 24a + 128 = 0 

a^2 – 8a – 16a + 128 = 0 

a(a – 8) -16(a – 8) = 0 
(a – 16)(a – 8) = 0

Either a = 8 or a  = 16


When a = 8, b = 16 and when a = 16, b = 8



Therefore the dimensions of the rectangle are:

8 cm by 16 cm

Answer 2

Answer:

8 cm and 16 cm

Step-by-step explanation:

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