I need help finding the solution

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Explanation:

If you apply the distance formula, you should find that triangle DEF has the following side lengths

Those distances are exact. The sqrt(50) approximates to 7.071

Since 7.071 is the longest side, we'll make c = sqrt(50)

Then we have a = 5 and b = 5

Note that a^2+b^2 = 5^2+5^2 = 50 while c^2 = (sqrt(50))^2 = 50

Both a^2+b^2 and c^2 are equal to 50.

That means a^2+b^2 = c^2 is a true equation for the a,b,c values mentioned.

By the converse of the pythagorean theorem, we have shown that triangle DEF is a right triangle.

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Side notes:

right

Step-by-step explanation:

we should find the distance of

DE

EF

FD

for DE

D(2,3) = (x1,y1)

E(5,7) = (x2,y2)

disatnce =

=

=

=

=

=5 units

for EF

E(5,7) = (x1 , y1)

F(9,4) = (x2 , y2)

distance =

=

=

=

=

=5 units

for DF

D(2,3) = (x1 , y1)

F(9,4) = (x2 , y2)

diatance =

=

=

=

=

=

It is a right angle triangle .

to prove right angle triangle

sum of square of two smaller sides = sum of square of longest side

5^2 + 5^2 =

25 + 25 = 52 *2

50 + 50

hence proved.

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm

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step-by-step explanation: