Solve the problems below. answer with completely simplified exact value(s) or expression(s). a) in δabc, ac = bc, cd⊥ab with d∈ab, ab = 4 in, and cd = 3 in. find ac. b) given: δabc, ab = bc = ac = a. find: the area of δabc

a) AC =

b) Area = ×

Step-by-step explanation:

a) From question,

                      AC = BC, CD⊥AB

Now in ΔCAD and ΔCBD

AC=BC, ∠A = ∠B and AD=BD (because in isosceles triangle perpendicular bisects the side).

then, from SAS potulates

                     ΔCAD≅ΔCBD

So,

    AD = = = 2 in

From Pythagorean theorem in ΔADC

= +

= +

= 4 + 9 = 13

AC =

b) In given ΔABC,

               AB = BC = AC = a,  means ΔABC is a equilateral triangle.

So, area of equilateral triangle is

                              Area = ×  

                                side = a

then,

       Area = ×              

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a

step-by-step explanation: