19. Length of a rectangle is x+2. breadth is x-2 and perimeter is 8 meters. Raju said that the area of a rectangle is 24 sq.m. Do you agree with him? and why?
Answers
Answer:
No , because value of x is 2 so , the length and breadth is 4 and 0 respectively . So its area will be 0 .
Answer:
I agree with Raju. Because his statement was true, the area of the rectangle is 24 cm².
Step-by-step explanation:
Given:
Length of the rectangle = x + 2
breadth of the rectangle = x - 2
Perimeter of the rectangle = 8 m
To find out:
To find out whether the area is 24 cm² or not.
Solution:
To find the area, we have to find the value of 'x'. We can find the value of 'x' in 2 ways.
⇒ The perimeter (P) of the rectangle is the sum of the 4 sides of the rectangle. Or 2 times the sum of the length (l) and breadth (b). That is,
P = 2(l + b)
By substituting,
2( x + 2 + x - 2) = 8
2(2x) = 8
4x = 8
Then, length = 2 +2 = 4 and breadth = 2 - 2 = 0. breadth can not be zero. Therefore, the value of 'x' can not be 2. The perimeter is not 8 m.
⇒ The area (A) of the rectangle is the product of length and breadth. That is,
A = l × b
= (x + 2) (x - 2)
= x² - 2²
= x² - 4
Raju said that the area of the rectangle is 24 cm². Then,
x² - 4 = 24
x² = 24 + 4 = 28
x = √28
= 5.291
∴ Length = 7.291
breadth = 3.291
I agree with Raju. Because his statement was true, the area of the rectangle is 24 cm².