Explanation:
first finding the area of the triangle by Heron's formula.
s=(a+b+c)/2, a=BC=5 unit, b=AC= 4√2unit, c=AB=7unit.
s=(5+4√2+7)/2 = (12+4√2)/2 =2( 6+2√2 )/2 = 6+2√2 unit .
Now, the Heron's formula : √s(s-a)(s-b)(s-c)
> √ (6+2√2)[(6+2√2)-5][(6+2√2)-4√2][(6+2√2)-7]
we have use √2's value ; 1.414 to simplify.
please simplify it with the help of calculator or doin it in a copy, because it is very difficult to share the full calculation. AFTER CALCULATION,
> √196.0000 > 14(units)².
Now, we know that the area of triangle is 14(units)². and another formula of finding the area of triangle is ½(base)(height). let the height be h.
Area = ½(base)(height)
=>14= ½(7)h. (after cross multiplication)
=>(14×2)/7=h. (after cancellation)
=>2×2=h.
=> 4units = h.
Therefore, CM that is the height is 4units.
I have every time written units because the unit is not given or you have not posted if given in the question you will write that unit only like cm or m anything like that.