Question

The length (L) of a photograph is 8mm longer than its width (W). Its perimeter (P) is more than 60mm. = +
a. Write an equation for the length in terms of the width L = _____________________
b. Use these expressions to write an inequality based on the given information.
c. Solve the inequality clearly indicating the length and width of the photograph.
d. Write your answer in a complete sentence

Answer 1

a) L = w + 8mm
b) Perimeter = 2(L + W) ; more than 60mm.

2(L + W) > 60
2(w + 8) + 2w > 60 
2w + 16 + 2w > 60
4w + 16 > 60     *expression of inequality

c) 4w + 16 > 60
         - 16    -16
    4w        > 44
   ÷4              ÷4
      w        > 11

Width is greater than 11. Assuming Width is 12mm then Length is 20mm (12 + 8)

d) The width should always be greater than 11mm, and length should always be 8mm longer than the width for its perimeter to be more than 60mm and prove the inequality to be true.

to check: assume w = 12
2(L + W) > 60
2(20 + 12) > 60
2(32) > 60
64 > 60