a Suppose that the side lengths of a triangle are a, b, and c, with c being the longest. If a^2+b^2>c^2, the triangle is an acute triangle.
B
b Suppose that the side lengths of a triangle are a, b, and c, with c being the longest. If a^2+b^2obtuse triangle.
A
aExample Integer: 13
B
bExample Integer: 16
Practice makes perfect
a Suppose that the side lengths of a triangle are a, b, and c, with c being the longest. If we compare a^2+b^2 to c^2, we can find the type of triangle these sides form.
The side lengths 9, 12, and 15 form a right triangle. Therefore, for 9, 12, and the integer number j to be the sides of an acute triangle, j must be greater than 9 and 12, but less than 15.
9 < 12 < j < 15
A number that satisfies these conditions is j=13. Let's verify that 9^2+12^2 is greater than 13^2.
Please note that we could have also assumed that 12 was the longest side and solved for a, so our answer is only one possible correct answer.
b In Part A we found that the given two side lengths, 9 and 12, and the number 15 form a right triangle. Therefore, for 9, 12, and the integer k to represent the side lengths of an obtuse triangle, k must be greater than 15.
9 < 12 < 15 < k
A number that satisfies this condition is k=16. Let's verify that 9^2+12^2 is less than 16^2.
