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
Share
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
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
24 will be the correct answer
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[tex]\sqrt{2}[/tex] 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[tex]\sqrt{2}[/tex])² = EB² + BE² [ BE and BC are equal ]
⇒ 9(2) = 2 EB²
⇒ 18 = 2 EB²
⇒ EB² = 9
⇒ EB = [tex]\sqrt{9}[/tex] = [tex]\sqrt{ (3)(3)}[/tex] = 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 = [tex]\sqrt{16}[/tex] = 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