Heya! Answer the following MCQ!
The diagonal is √41 cm and its area is 20 cm². The perimeter of the rectangle must be :
a. 9 cm
b. 18 cm
c. 20 cm
d. 41 cm
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Answers
Answer:
option b. 18
Step-by-step explanation:
V(l² + b²) = V41
also, lb = 20
(l+b)² = (l²+b²)+2/b = 41+40 = 81
= (l + b)=9
: perimeter = 2(l + b)= 18cm
Answer:
option b) 18 cm
Step-by-step explanation:
Given :
- The diagonal of the rectangle is √41 cm
- The area of the rectangle is 20 cm²
To find :
the perimeter of the rectangle
Solution :
Let the length of the rectangle be l cm and breadth of the rectangle be b cm
In a rectangle, the square of the diagonal is equal to the sum of the squares of the length and breadth.
diagonal² = length² + breadth²
(√41)² = l² + b²
41 = l² + b² ⟼ [1]
Area of the rectangle = length × breadth
20 cm² = l × b
lb = 20 ⟼ [2]
we know,
(a + b)² = a² + b² + 2ab
Similarly,
(l + b)² = l² + b² + 2lb
(l + b)² = 41 + 2(20) (eqn. [1] & [2])
(l + b)² = 41 + 40
(l + b)² = 81
(l + b) = √81
(l + b) = 9 cm
Perimeter of the rectangle = 2(length + breadth)
Perimeter = 2(l + b)
Perimeter = 2(9 cm)
Perimeter = 18 cm
Therefore, the perimeter of the rectangle is 18 cm
