△ABC is a right triangle with right angle C. Side AC¯¯¯¯¯¯¯¯ is 6 units longer than side BC¯¯¯¯¯¯¯¯. If the hypotenuse has length 217−−√ units, find the length of AC¯¯¯¯¯¯¯¯.

Given:

In △ABC is a right angle triangle.

AC is 6 units longer than side BC.

To find:

The length of AC.

Solution:

Let the length of BC be x.

So, Length of AC = x+6

According to the Pythagoras theorem, in a right angle triangle

△ABC is a right angle triangle and AC is hypotenuse, so

Subtract 68 from both sides.

Divide both sides by 2.

Splitting the middle term, we get

Side cannot be negative, so x=2 only.

Now,

Therefore, the length of AC is 8 units.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.