If de = 37 cm and ef = 16 cm, then what are the possible lengths for df so that de, ef, and df can form a triangle? explain your reasoning.

The length of DF must be between 21 and 53.

Step-by-step explanation:

In a triangle, the length of two sides added together must exceed the length of the 3rd side. So, since EF is the shortest of the two givens, we know that EF + DF must be greater than DE. So we can plug in these numbers to find the minimum.

EF + DF > DE

16 + DF > 37

DF > 21

Now, for the upper maximum, we know that the two given lengths must be greater than the length of DF. So again, we can solve for the maximum using the amounts.

DE + EF > DF

37 + 16 > DF

53 > DF

With these two in mind, we know that DF must be between 21 and 53

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.