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Answers
Answer:
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Answer:
The length, area and the perimeter of the rectangle are 21cm, 420 cm² and 82 cm respectively.
Step-by-step explanation:
Let the rectangle be ABCD.
According to the question :
➟ Diagonal : BD = 29cm
➟ Breadth : CD = 20cm
All the angles in a rectangle are 90°.
So, ∆BDC is a right angled triangle with ∠BCD = 90°. Using pythagoras theorem :
➟ (P)² + (B)² = (H)²
➟ (BC)² + (20)² = (29)²
➟ BC² + 400 = 841
➟ BC² = 841 – 400
➟ BC² = 441
➟ BC = √441
➟ BC = 21cm
∴ The length of the rectangle BC is 21 cm.
Now, let's find the area of the rectangle :
➟ Area of rectangle = Length × breadth
➟ A = 21cm × 20cm
➟ Area = 420cm²
∴ The area of the rectangle is 420 cm².
Finally, finding the perimeter of the rectangle :
➟ Perimeter = 2 (l + b)
➟ P = 2 (21cm + 20cm)
➟ P = 2 (41cm)
➟ Perimeter = 82cm
∴ The perimeter of the rectangle is 82 cm.
Explanation: