Question

Use the patterns you found to predict whether each set of lengths below will form a triangle. If a set will form a triangle, state whether the triangle will be acute, obtuse, or right. Justify your conclusion. a. 5 cm, 6 cm, and 7 cm b. 2 cm, 11 cm, 15 cm c. 10 cm, 15 cm, 20 cm d. 10 cm, 24 cm, 26 cm e. 1 cm, 3 cm, 9 cm f. 2 cm, 10 cm, 11 cm Core Connections, Course } 412

Answer 1

Answer with Step-by-step explanation:

We have to find given length set form a triangle and find the type of triangle acute, obtuse or right.

If sum of length of any two sides is greater than the length of third side then the given side length form a triangle otherwise not.

a.5 cm, 6 cm and 7 cm

`5+6=11cm  > 7cm`

Hence, given set of side length form a triangle.

`5^2+6^2=25+36=61 >7^2=49`

Hence, given triangle is acute triangle.

b.2 cm,11 cm,15 cm

`2+15=17 cm > 11 cm`

Hence, given side length set form a triangle.

`2^2+11^2=4+121=125 < (15)^2=225`

Hence, the triangle is an obtuse triangle.

c.10 cm,15 cm,20 cm

`10+15=25 cm >20 cm`

Hence, given set of length side form a triangle.

`(10)^2+(15)^2=225 >(20)^2=400`

Hence, the triangle is an acute triangle .

d.10 cm,24 cm,26 cm

`10+24=34 cm > 26 cm`

Hence, given set of side length form a triangle.

`(10)^2+(24)^2=676=(26)^2=676`

Hence, the triangle forms a right triangle.

e.1 cm,3 cm, 9 cm

`1+9=10 cm > 3 cm`

Hence, the given set of side length forms a triangle.

`1^1+3^2=10<9^2=81`

Hence, the triangle is an obtuse triangle.

f.2 cm, 10 cm,11 cm

`2+10=12 cm > 11cm`

Hence, the given set of side length set forms a triangle.

`2^2+(10)^2=104<(11)^2=121`

Hence, the triangle is an obtuse triangle.