Given: ΔABC, CM⊥AB, BC = 5, AB = 7, CA = 4√2

Find: CM

Step-by-step 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.

step-by-step explanation: