#12**+16 **

I think the answer is 15*sqrt3+15

Now let me try and explain how I got this.

< KJA = 60° Ext < of a triangle is equal sum of opposite interior angles

triangle JKF is isosceles (2 equal angles) therefore KJ=JF=10

consider triangle AJK

Sin30=1/2=AJ/10 so AJ=5

Using Pythagoras' Theorum

$$AK^2=10^2-5^2

AK^2=100-25

AK^2=75

AK=5\sqrt3$$

AF=5+10=15

$$\\KF^2=15^2+(5\sqrt3)^2\\\\

KF^2=225+75\\\\

KF^2=300\\\\

KF=10\sqrt3\\\\$$

$$\\Perimeter = 5\sqrt3+10\sqrt3+15\\\\

Perimeter = 15\sqrt3+15\;\; units\\\\$$

Melody
Jul 10, 2014

#1**0 **

A triangle has 180 degrees, right. So you add 30+30=60. So, the perimeter is 180 degrees.

DragonSlayer554
Jul 9, 2014

#5**0 **

Well, I don't know how to find the perimeter of a triangle using degrees.

DragonSlayer554
Jul 9, 2014

#6**+6 **

Converse of the base angle theorem - If two angles of a triangle are congruent, then the sides opposite those angles are congruent

Rose98
Jul 9, 2014

#9

#11**+8 **

sorry i took so long ive been away but i believe the answer is 41.03 only because if you look at the formula or a diagram for a 30,60,90 triangle the smaller leg is X the second leg is x square root3 and the hypotenuse is 2x using these if you fine the perimeter for KAJ you can also use the same formulas on the larger triangle that you need hope im right lol

snip3s
Jul 10, 2014

#12**+16 **

Best Answer

I think the answer is 15*sqrt3+15

Now let me try and explain how I got this.

< KJA = 60° Ext < of a triangle is equal sum of opposite interior angles

triangle JKF is isosceles (2 equal angles) therefore KJ=JF=10

consider triangle AJK

Sin30=1/2=AJ/10 so AJ=5

Using Pythagoras' Theorum

$$AK^2=10^2-5^2

AK^2=100-25

AK^2=75

AK=5\sqrt3$$

AF=5+10=15

$$\\KF^2=15^2+(5\sqrt3)^2\\\\

KF^2=225+75\\\\

KF^2=300\\\\

KF=10\sqrt3\\\\$$

$$\\Perimeter = 5\sqrt3+10\sqrt3+15\\\\

Perimeter = 15\sqrt3+15\;\; units\\\\$$

Melody
Jul 10, 2014

#14**+13 **

JF = KJ = 10 Sides opposite equal angles are themselves equal

Therefore, m<KJF = 120

m<KJF = 120 Therefore m< KJA = 60 (The sum of any two angles comprising a strainght angle = 180)

Therefore, triangle KAJ is 30 - 60 - 90

And AJ = 5 And KA = 5√3

Then, by the Pytagorean theorem, KF = √[ (AJ + JF)^2 + (KA)^2] = √[ (5 + 10)^2 + (5√3)^2] =

√[ (15)^2 + (5√3)^2] = √[ 15^2 + 75] = √[ 225 + 75] = √[ 300] = 10√3

So....the perimeter = AJ + JF + KF + KA = 5 + 10 + 10√3 + 5√3 =

15 + 15√3

CPhill
Jul 10, 2014