Question

Work out the dimensions of rectangles A and B

Answer 1

Area of the square=36cm^2

Let the length of its side be a.

According to the question, 36=a^2

=>a=+/-6

Since dimension cant be negative, a=-6 has to be ignored. Thus, a=6cm

Since the areas of two rectangles A and B are in the ratio 2:1, let them be 2x cm^2 and x cm^2 respectively. According to the question,

Total area of the two rectangles = 36 cm^2

2x+x=36

=> 3x=36

=>x=36/3=12

Ar(rect. A) = 2x = 2×12= 24cm

Ar(rect. B) = x = 12cm

It is noticed that length of A = length of B = length of side of square = 6cm

So, in rectangle A, area= length × breadth

=> 24=6×breadth

=>breadth =24/6 = 4cm

Also, in rectangle B, area = length ×breadth

=> 12= 6×breadth

=> breadth= 12/6= 2cm

Thus, (1) in rectangle A, length =6cm; breadth=4cm

(2) in rectangle B, length = 6cm; breadth= 2cm

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