Question

A (15) Lesson Quiz- Pythagorean TheoremClassify each triangle according to the lengths given.The sides of a triangle havelengths 3, 5, and 6The sides of a triangle have lengths 6, 9,and 9The sides of a triangle havelengths 3, 4, and 6The sides of a triangle have lengths 9, 12,and 15

Answer 1

Given:

There are 4 triangles given with length of sides.

Required:

We need to find that which triangle is Pythagorean triangle means right angled triangle

Explanation:

Pythagorean theorem:

square of Longest side is equal to the addition of square of other two sides.

1) The sides of a triangle have lengths 3, 5, and 6

here longest side is 6 so by Pythagorean theorem

$6^2=36$

now for other two sides

$3^2+5^2=9+25=34\ne36$

Not a Right angled triangle

2) The sides of a triangle have lengths 6, 9 and 9

As we can see that there are two sides of triangle are equal

so this triangle is Isosceles triangle

3) The sides of a triangle have lengths 3, 4, and 6

Here longest side is 6

$6^2=36$

now for other two sides

$3^2+4^2=9+16=25\ne36$

now a Right angled triangle

4) The sides of a triangle have lengths 9, 12 and 15

Longest side is 15

$15^2=225$

Now for other two sides

$9^2+12^2=81+144=225$

This triangle is Right angle triangle

Final answer:

Only the last triangle is right angled triangle