Which set can not reprsent the lengths of the sides of a triangle?
a){4,5,6} 2){5,5,11) 3){7,7,12} 4){8,8,8}
The coordinates of Point R are (-3,2) and the coordinates of point T are (4,1). What is the length of RT?
to have a triangle, the sum of any two of the sides must be greater than the third side.
so look at 5,5,11, is 5+5 > 11 ?
for the second, use your "distance between two points" formula.
http://www.purplemath.com/modules/distform.htm
look at the example half way down the page, it fits your problem exactly.
To determine whether a set of numbers can represent the lengths of the sides of a triangle, we need to check if it satisfies the triangle inequality theorem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.
1) {4,5,6}: 4 + 5 = 9 > 6. Also, 4 + 6 = 10 > 5. And, 5 + 6 = 11 > 4. So, this set can represent the lengths of the sides of a triangle.
2) {5,5,11}: 5 + 5 = 10 > 11 is false. So, this set cannot represent the lengths of the sides of a triangle.
3) {7,7,12}: 7 + 7 = 14 > 12 is true. So, this set can represent the lengths of the sides of a triangle.
4) {8,8,8}: 8 + 8 = 16 > 8 is true. So, this set can represent the lengths of the sides of a triangle.
Therefore, the set that cannot represent the lengths of the sides of a triangle is 2) {5,5,11}.
To find the length of RT, we can use the distance formula, which is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point R are (-3,2) and the coordinates of point T are (4,1).
Using the distance formula:
RT = √((4 - (-3))^2 + (1 - 2)^2)
= √((4 + 3)^2 + (-1)^2)
= √(7^2 + 1)
= √(49 + 1)
= √50
= 5√2
Therefore, the length of RT is 5√2.