How do I find a ratio of (a) the perimeters and (b) the areas of each pair of figures? Can someone guide me through this problem?  A rectangle with length...

How do I find a ratio of (a) the perimeters and (b) the areas of each pair of figures?

Can someone guide me through this problem?  A rectangle with length 12cm and perimeter 30cm, and a rectangle with

length 10cm and perimeter 30cm.

I also need some assistance on this problem.

 Concrete can be made by mixing cement, sand, and gravel in a 3:6:8 ratio.

How much gravel is needed to make 850cm2 of concrete?

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gsarora17 | (Level 2) Associate Educator

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1) Given Length of First Rectangle (L1) = 12 cm and Length of Second Rectangle L2=1O cm

Perimeter of First Rectangle (P1) = 30 cm  , Perimeter of Second Rectangle(P2)=30 cm

Let B1 and B2 be the breadths of the two rectangles

We know that Perimeter of Rectangle = Sum of all sides

                                                      = 2( Length + Breadth)

Therefore P1 = 2( L1+B1) 

              30= 2(12+B1) = 24+2B1

2B1=30-24=6

B1= 3 cm

P2= 2(L2+B2)

30=2(10+B2) = 20+2B2

2B2=30-20=10

B2=5 cm

Now Area of Rectangle = Length x Breadth

Therefore Area of First Rectangle (A1) = L1 X B1= 12 X 3 = 36 sq.cm

Area of Second Rectangle (A2) = L2 X B2 = 10 X 5 = 50 sq.cm

Ratio of Perimeter = P1/P2 = 30/30 = 1

Ratio of Area = A1/A2 = 36/50 =18/25 = 0.72

2) It is given that the ratio of Cement : Sand : Gravel = 3:6:8

Sum of the ratios = 3+6+8 = 17

Therefore Gravel needed to make 850 sq.cm concrete = (8/17) x 850

                                                                             = 8 x 50

                                                   Gravel needed      = 400 sq.cm. 

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