Question

In each question,first make an inequality, then solve the inequality

1) A rectangle is 8cm long and b cm broad.find the range of values of b if the perimeter of the rectangle is not greater than 50 cm and not less than 18cm
2) the sides of a triangle are x cm,x+3 cm, find the lowest value of x.​

Answer 1

a) The perimeter of a rectangle is written as:

P = 2*L + 2*W

where L is the length amd W is the width (broad in this case).

here we have:

L = 8cm and W = b

then the perimeter is:

P = 2*8cm + 2*b

And we know that:

18cm ≤ P ≤ 50cm

where ≤ is used because there is written "not more" and "not less", so the equalities are allowed

now we can replace P by the above equation:

18cm ≤ 16cm + 2*b ≤ 50cm

now we can subtract 16cm in each side and get:

18cm - 16cm ≤ 2*b ≤ 50cm - 16cm

2cm ≤ 2*b ≤ 34cm

Now we can divide each side by 2.

1cm ≤ b ≤ 34cm/2 = 17cm

1cm ≤ b ≤ 17cm.

b) Here we have missing information, so this can not be answered.

(only knowing that one side length is x, and another side length is x + 3cm, we can know that x > 0cm, so the minimum value of x is really close to 0cm)