Trying to find length and area from this triangle.

24, 204

Step-by-step explanation:

to find the height

we would use the heron formula  when all the sides are given

S which is equal to half of the perimeter of the triangle which is (a+b+c)/2.

S = (17+ 25+ 26)/2 = 68/2 = 34

Area = √S(S-A)(S-B)(S-C)

Area= (1/2)bh

we equate it back to the formula Area = √S(S-A)(S-B)(S-C)

it becomes

(1/2)bh  = √S(S-A)(S-B)(S-C)

A = IABI= 25

B= IBCIM = 26

C= IACI = 17

b = base = IACI = 17

S = 34

(1/2)bh  = √S(S-A)(S-B)(S-C)

(1/2)17h  = √34(34-25)(34-26)(34-17)

(17/2)h = √34(9)(8)(17) = √34 x 9 x 8 x 17

(17/2)h = √41616 = 204

17h/2 = 204

17h = 204 x 2 = 408

h = 408/17 = 24 inch

height = h = IBDI = 24 in

Area = (1/2)bh

      = (1/2) x 17 x 24

    =  12 x 17 = 204  or we use the heron formula just like the above which we get 204 before multiplication by 2.