a rectangle is 8cm long and bcm broad. find the range of values of b if the perimeter is not greater than 50cm and not less than 18cm
18 cm ≤ 2b + 16 cm ≤ 50 cm
subtracting 16 ... 2 cm ≤ 2b ≤ 34 cm
dividing by 2 ... 1 cm ≤ b ≤ 17 cm
It is correct 👍👍👍👍
Why did the rectangle go on a diet? Because it wanted to stay within the "perimeter" of 50cm!
But seriously, let's solve this math problem. The perimeter of a rectangle is calculated by adding all four sides together. In this case, we have a length of 8cm, a breadth of b cm, and a perimeter that needs to be between 18cm and 50cm.
To find the range of possible values for b, we need to set up an inequality. The inequality for the perimeter can be written as:
2(8 + b) ≤ 50
Simplifying this inequality, we get:
16 + 2b ≤ 50
Subtracting 16 from both sides:
2b ≤ 34
Dividing both sides by 2:
b ≤ 17
Therefore, the range of possible values for b is less than or equal to 17cm.
To find the range of values for b, we need to consider the perimeter of the rectangle. The perimeter of a rectangle is given by the formula:
Perimeter = 2(Length + Breadth)
Given that the length of the rectangle is 8cm, we can rewrite the formula as:
Perimeter = 2(8 + b)
Now we have an equation for the perimeter. We know that the perimeter should not be greater than 50cm and not less than 18cm.
To find the range of values for b, we need to solve the equation for both the upper and lower limits.
1. Upper limit:
Setting the perimeter equal to the upper limit of 50cm:
50 = 2(8 + b)
25 = 8 + b
b = 25 - 8
b = 17
Therefore, the upper limit for b is 17cm.
2. Lower limit:
Setting the perimeter equal to the lower limit of 18cm:
18 = 2(8 + b)
9 = 8 + b
b = 9 - 8
b = 1
Therefore, the lower limit for b is 1cm.
Thus, the range of values for b is 1cm ≤ b ≤ 17cm.