the length of the sides of a triangle are consecutive odd numbers what is the length of the longest side if the perimeter is 45 in easy method with formulae?
Answers
Answer:
Explanation:
We can convert this into a slightly more abstract problem as follows:
For "perimeter" we can read "sum"
For "lengths of the sides of a triangle" we can read "three numbers"
If the middle of the three consecutive odd integers is
n
, then the smallest is
n
−
2
, the largest is
n
+
2
and we have:
45
=
(
n
−
2
)
+
n
+
(
n
+
2
)
=
3
n
Hence
n
=
45
3
=
15
and the largest of three numbers (i.e. the length of the longest side of the triangle in inches) is
n
+
2
=
15
+
2
=
17
Step-by-step explanation:
Answer:We can convert this into a slightly more abstract problem as follows:
For "perimeter" we can read "sum"
For "lengths of the sides of a triangle" we can read "three numbers"
If the middle of the three consecutive odd integers is
n
, then the smallest is
n
−
2
, the largest is
n
+
2
and we have:
45
=
(
n
−
2
)
+
n
+
(
n
+
2
)
=
3
n
Hence
n
=
45
3
=
15
and the largest of three numbers (i.e. the length of the longest side of the triangle in inches) is
n
+
2
=
15
+
2
=
17
Step-by-step explanation: