Question

the square show below has been divided into four rectangles. if the side of each of the segments in the diagram is an integer and the areas of two rectangle are 192cm and 1152 cm, the find the difference between areas of two other rectangle​

Answer 1

Answer:

regular hexagon AB1F1DF2B2A

AB1 = B1F1 = F1D = DF2 = F2B2 = B2A = 30 cm

∠B2AB1 = ∠AB1F1 = ∠B1F1D = ∠F1DF2 = ∠DF2B2 = ∠F2B2A = 120°

Δ AB1G and Δ AB2G are the two equal halves of one rectangle.

and Δ F1DH and Δ F2DH are two equal halves of another rectangle.

⇒ ∠B1AG = ∠B2AG

Now, ∠B1AB2 = ∠B1AG + ∠B2AG = 120°

⇒ ∠B1AG = ∠B2AG = 60°

In Δ AGB1,

∠AGB1 + ∠AB1G + ∠GAB1 = 180°

⇒ 90° + 60° + ∠GAB1 = 180°

⇒ ∠GAB1 = 30°

We know that sides of any triangle of angles 30°, 60° and 90°

are in the ratio 1:√3:2.

⇒ AG : B1G: AB1 = 1: √3: 2

⇒ AG: B1G: 30 = 1: √3: 2

⇒ AG = 15 cm and B1G = 15√3 cm

Similarly, In Δ AB1B2

⇒ B1B2 = B1G + B2G = 2(B1G) = 2(15√3) cm = 30√3 cm

∴ For small rectangles :

Length = B2G = B1G = 15√3 cm

Breadth = AG = 15 cm

∴ For rectangle B1B2 H2H1 :

Length = B1B2 = 30√3 cm

Breadth = B1F1 = 30 cm

Length and Breadth of rectangles in cm are

(15√3 ,15),(15√3, 15) and ( 30√3, 30).