Question

3.6.79 Skill Builder 3 Question Help The perimeter of a rectangle is 38 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 60 square feet. Express the possible lengths of a side. (Type your answer in interval notation.) Enter your answer in the answer box and then click Check Answer.

The answer must be in interval notation.

I know the possible lengths come up as 15 and 4. That is not the full answer.

Answer 1

x feet feet =38 19 xy = 60 het length of rectangle be breadth of rectangle be 8 perimeter of re Jangle = 2 (4+b) = 2(x+y) Area of rectangle = length a breadth = xy Now it is given that perimeter =38 feet Hence 2(x+y) = 38 xty xty = 19 y = 19-x Again it is given that area of rectangle is not to exceed 60 squere foot gut means area of rectangle < 60 feet2 Hence XC19-) <60 19x-x² <60 - x² +19x = 60 Divided both side by x² - 19x7-60 x² - 19x+6070 By factori sing the inequelities by splitting the middle term. XP-15 Y-4X+60 > 0 x(x-15) -4(0-150 (3-4) (X-1570 x-uzo and X-1570 there fore x = 4 x = 15 if x=4 then y = 19 x = 19.4=15 since length will never be greater than breadth Hence x 74 mean x=4 is not admissible if x = 15 then y = 19-1 =19-15=4 Since perimeter =38 feet, means x+y=1g Hence Final answer length is feet, breadth sy Hence if x 15 then ys 9