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Pls help!!
I'll give brainliest!
find the perimeter and area of the equilateral triangle withh sides A(2b+8)cm , B(2a-b)cm and C(a+5)cm​

Pls Help Ill Give Brainliest Find The Perimeter And Area Of The Equilateral Triangle Withh Sides A2b8cm B2abcm And Ca5cm class=

Sagot :

Answer:

P = 36 cm.   A = 36[tex]\sqrt{3}[/tex]  sq. cm.   or 60.62

Step-by-step explanation:

Equilateral triangle (all sides are =)

2b + 8 =  2a - b                   a + 5 = 2a - b

       8 = 2a - 3b                        5 = a - b

Solving as a system of equation  

    8 = 2a - 3b        Do not change

    5 =   a - b           Multiply by -3

   8 = 2a - 3b

-15 = -3a +3b

   7 = a          

 Solve for b:  8 = 2a - 3b        

                      8 = 2(7) - 3b

                      8 = 14 - 3b

                      -6 = -3b

                       2 = b

What is the length of a side : 2(b) +8 = 2(2) + 8 ;  4 + 8 = 12

                                                  a + 5 = 7 + 5  = 12

                                                  2a - b = 2(7) - 2; 14 - 2 =12

P = 3 (sides); P = 3 (12); P = 36 cm.

A = 1/2bh , in this equilateral triangle the sides are 12 cm. So the base of the triangle is  12 and the height is 6[tex]\sqrt{3}[/tex].   ( draw the height from point A to the midpoint of CB, and you have a 60 30-90 Δ    Long leg equal short leg [tex]\sqrt{3}[/tex].      A = 1/2 (12)(6[tex]\sqrt{3}[/tex]) ;  A = 6(6[tex]\sqrt{3}[/tex]) ;  A = 36[tex]\sqrt{3}[/tex] square cm

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