MATHEMATICS HIGH SCHOOL

20 POINTS FOR 3 QUESTIONS!!!!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°

Answers

Answer 1

Answer:

Answer with Step-by-step explanation:

1.In triangle ABC

AB=BC

Let AB=BC=x and AC=y

Perimeter of triangle ABC=25

$x+x+y=25$

$2x+y=25$ ...(1)

$x-y=4$ ...(2)

Adding equation (1) and (2)

$3x=29$

$x=(29)/(3)=9.67$

Substitute x=9.67 in equation (2)

$9.67-y=4$

$y=9.67-4=5.67$

$AB=BC=9.67$

$AC=5.67$

2. $m\angle R=2x+11$

$m\angle S=3x+23$

$m\angle T=x+42$

$m\angle R+m\angle S+m\angle T=180^(\circ)$

By using triangle angle sum property

Substitute the values then we get

$3x+42+4x-11+x+13=180$

$8x+44=180$

$8x=180-44=136$

$x=(136)/(8)=17$

Substitute the value

$m\angle R=3(17)+42=93^(\circ)$

$m\angle S=4(17)-11=57^(\circ)$

$m\angle T=17+13=30^(\circ)$

$m\angle R>m\angle S$

$m\angle S>m\angle T$

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

$RT>RS$ (side RS is opposite to angle T)

When a>b

Then , opposite side of a> opposite side of b

RS<RT<ST

3. $m\angle R=2x+11$

$m\angle S=3x+23$

$\angle T=x+42$

$m\angle R+m\angle S+m\angle T=180^(\circ)$

By using triangle angle sum property

Substitute the values then we get

$2x+11+3x+23+x+42=180$

$6x+76=180$

$6x=180-76$

$6x=104$

$x=(104)/(6)=17.3$

Substitute the value

$m\angle R=2(17.3)+11=45.6$

$m\angle S=3(17.3)+23=74.9$

$m\angle T=17.3=42=59.3$

$m\angle S>m\angle T$

$m\angle T>m\angle R$

RT>RS

RS>ST

ST<RS<RT

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Answers

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