20 points for 3

given: ∆abc, ab = bc, m∠1< 90°

perimeter of ∆abc = 25

difference between the two sides is 4

find: ab, bc, ac

list the sides of δrst in in ascending order (shortest to longest) if:

m∠r = 3x+42°, m∠s = 4x−11°, and m∠t = x+13°

list the sides of δrst in in ascending order (shortest to longest) if:

m∠r = 2x+11°, m∠s = 3x+23°, and m∠t = x+42°

Answer with Step-by-step explanation:

1.In triangle ABC

AB=BC

Let AB=BC=x and AC=y

Perimeter of triangle ABC=25

...(1)

...(2)

Adding equation (1) and (2)

Substitute x=9.67 in equation (2)

2.

By using triangle angle sum property

Substitute the values then we get

Substitute the value

(Side ST is opposite to angle R, Side RT is opposite to angle S

 (side RS is opposite to angle T)

When a>b

Then , opposite side of a> opposite side of b

RS<RT<ST

3.

By using triangle angle sum property

Substitute the values then we get

Substitute the value

RT>RS

RS>ST

ST<RS<RT

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.