Question

In the given image if BCDE is a square, then what is the area of the biggest rectangle in cm?
5 cm
3.2 cm
A
16
21
24​

Answer 1

Answer:

24 will be the correct answer

Answer 2

Answer:

area of the biggest rectangle = 21 cm²

Step-by-step explanation:  

Given data

In given image BCDE is a square

AB = 5 cm and  EC =  3$\sqrt{2}$ cm  

⇒ here we need to find area of the biggest rectangle which is rectangle  FDCA  

If we observe the figure EBC and EBA  are right angled triangles and EB and BC are equal sides

From Pythagoras theorem in right angled triangle EBC  

⇒  hypotenuse² = side² + side²  

⇒                 EC² = EB² + BC²  

⇒              (3$\sqrt{2}$)² = EB² + BE²                [ BE and BC are equal ]

⇒                 9(2)  = 2 EB²    

⇒                    18 = 2 EB²

⇒                  EB²  =  9

⇒                  EB    =  $\sqrt{9}$  = $\sqrt{ (3)(3)}$  = 3 cm

⇒             EB = 3 cm  and BC = 3 cm  

⇒ here BCDE is a square DC = ED = 3 cm  

In right angled triangle EBA    

⇒          AE² = EB² + AB²  

⇒           5²  =  3²+ AB²  

⇒           AB² = 25 - 9

⇒           AB   = $\sqrt{16}$  =  4      

⇒ In ACDF rectangle AC = AB + BC  

                             ⇒   AC = 4  + 3  

                             ⇒   AC = 7 cm  

⇒  and we know that DC = 3 cm

⇒ area of the rectangle ACDF = bh = 7 × 3 =  21 cm