Question

Sandy made a reflective sticker for her bicycle in the shape of a triangle. Two of the three side lengths
were 4 cm and 5 cm.
(a) Could the third side of the reflective sticker be 7 cm long? Explain your reasoning.
(b) Could the third side of the reflective sticker be 2 cm long? Explain your reasoning.
(c) Sandy decides to make the reflective sticker in the shape of an isosceles triangle. How many unique
shapes for the sticker are possible?
Use a sketch to show your reasoning. Label each side length.
@iGreen @Jaynator495 @jim_thompson5910

Answer 1

The two sides are 4 and 5. Let x be the length of the third side. It's unknown for now.

Answer 2

It turns out that x is both greater than the difference of the two sides

x > 5-4
x > 1

also, x is smaller than the sum of the two sides

x < 5+4
x < 9

So combined, x is between 1 and 9 and we write it as this compound inequality

1 < x < 9

x cannot equal 1 and it cannot equal 9. It can equal any number between 1 and 9

Answer 3

Oh ok that makes so much sense thank you @jim_thompson5910

Answer 4

That should take care of (a) and (b). Do you see how to do (c)?

Answer 5

Actually I don´t...

Answer 6

@jim_thompson5910

Answer 7

What does it mean when a triangle is an isosceles triangle?

Hint: it deals with the side lengths in some way

Answer 8

It is a triangle with at least two equal sides

Answer 9

@jim_thompson5910

Answer 10

yes

Answer 11

so if 2 of the sides are 4 and 5, then what could be x (the third side) if we have an isosceles triangle?

Answer 12

Either 4 or 5 right?

Answer 13

yes

Answer 14

possibility #1
side1 = 4 (given)
side2 = 5 (given)
side3 = 4


possibility #2
side1 = 4 (given)
side2 = 5 (given)
side3 = 5

Answer 15

That makes so much sense thank you so much.

Answer 16

sure thing