Question

for each triangle list the sides in order from shortest to longest explain your reasoning with words or numbers for the order

Answer 1

a. For the first triangle ,

Two angles are given. To determine the third angle apply the property of triangle which is sum of the angles of the triangle is 180 degree.

`27^(\circ)+82^(\circ)+\angle T=180^(\circ)`
`\angle T=180^(\circ)-27^(\circ)-82^(\circ)=71^(\circ)`

The triangle angles and sides relationship-

The longest side of a triangle is opposite the biggest angle measure.

The shortest side of a triangle is opposite the smallest angle measure in a triangle.

Therefore,

The shortest side is side opposite to the smallest angle that is MT.

The largest side is side opposite to the largest angle that is AT.

Hence the order for the sides from shortest to largest is

`14x+12=180`
`14x=168`
`x=12`

The angles obtained are

`(8x-1)=95,(3x+4)=40,(3x+9)=45`

We know that the longest side of a triangle is opposite the biggest angle measure.

The shortest side of a triangle is opposite the smallest angle measure in a triangle.

Hence the shortest side is JK and largest side is JL.

Hence the order for the sides from shortest to largest is

[tex]JK