Is the triangle with sides of the given lengths a right triangle?

Question

6, 9, 12 and 40, 75, 85

Explain why or why not.

Answer 1

Only if a^2 + b^2 = c^2 (where c is the largest side)

check: 6,9,12
6^2 + 9^2 = 36 + 81 = 117 not=12^2 = 144

check 40, 75, 85

40^2 + 75^2
= 1600 + 5625
= 7225
85^2 = 7225
YEP

40,75, 85 is because a^2 + b^2 = c^2

Answer 2

Let the sides of the triangle be a, b, and c such that a < b < c.

If a^2 + b^2 = c^2, then the triangle is a right triangle.

If a^2 + b^2 < c^2, then the triangle is an obtuse triangle.

If a^2 + b^2 > c^2, then the triangle is an acute triangle.

If sides are 6, 9, 12, then 6^2 + 9^2 < 12^2. The triangle is obtuse.

If sides are 40, 75, 85, then 40^2 + 75^2 = 85^2. The triangle is right. Notice that this triangle is the eighth multiple of the 8,15,17 pythagorean triple.

In trigonometry, the Law of Cosines can be used to explain the relationship between side lengths and the largest angle of a triangle.

Answer 3

For right angle triangle c^2 = a^2 + b^2 where c is the longest length

Now 12^2 = 144
9^2 = 81
6^2 = 36
81 + 36 = 117 not 144 so not right angle triangle

2nd question
85^2 = 7225
75^2 = 5625
40^2 = 1600
5625 + 1600 = 7225 so this is a right angle triangle

Answer 4

Right-angled triangles with lagest side c and other sides a and b must obey c^2 = a^2 + b^2.
12*12=144 is not 6*6 + 9*9 =117
so NO
85 squared is 7225; 40 sqd is 1600 and 75 sqd is 5625,
so YES

Answer 5

In a right triangle, Pythagoras's formula should be true.

a^2 + b^2 = c^2 where c is the longest side and a and b are the other two sides.
In the first case:

36 + 81 <> 144, so it isn't a right triangle.

the second:

1600 + 5625 == 7225, so it is!!

Answer 6

pythagorean theory.....if the sides of a right triangle have lengths a,b,c and c is hypotenuse, then a^2+b^2=c^2.
6,9,12....36+81 do not equal 144
40, 75, 85, 1600+5675=7225

Answer 7

"40-75-85"-triangle is the right one.
40^2+75^2=85^2

The first triangle doesn't meet this criteria.
Pythagorean theorem.

Answer 8

Two ways of doing this.

1. Substitute into Pythagoras a² + b² = c² and show it works or doesn't work

2. Use Pythagorean triples

(b) 40,75,85 is a multiple of 8, 15, 17 which is a standard triple

Answer 9

6, 9, 12
No. 36 + 81 < 144

40, 75, 85
Yes.
1600 + 5625 = 7225

Answer 10

the first is not a right angled triangle
because the sum of squares of the smaller sides donot give the square of the largest.............Pythagorous theorem
and the second is a right angled triangle
because it satisfies the Pythogorous theorem