Please help me. Thank you

I'll answer problem 19

Part (a)

The tickmarks on segments DE and DC indicate they are the same length. We're also told that |DC| = |DE| = 5.

So DE is also 5 cm long. Triangle DAE is a right triangle with the 90 degree angle at angle A. Let x be the length of segment AE.

We'll use the pythagorean theorem to find x

a^2 + b^2 = c^2

(AE)^2 + (AD)^2 = (DE)^2

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 25-16

x^2 = 9

x = sqrt(9)

x = 3

Segment AE is 3 cm long

Part (b)

For any rectangle, the opposite sides are parallel and the same length. This means AB = DC = 5 cm.

We found earlier that AE = 3 cm, so,

AE+EB = AB

3+EB = 5

EB = 5-3

EB = 2

Segment EB is 2 cm long

Part (c)

We know that AD = BC = 4 cm, because the opposite sides are the same length.

Earlier in part (b), we found that segment EB was 2 cm long.

Triangle EBC is a right triangle with legs EB = 2 and BC = 4. Let's apply the pythagorean theorem to find EC. Let y = EC.

a^2 + b^2 = c^2

(EB)^2 + (BC)^2 = (EC)^2

2^2 + 4^2 = y^2

4 + 16 = y^2

20 = y^2

y^2 = 20

y = sqrt(20)

y = sqrt(4*5)

y = sqrt(4)*sqrt(5)

y = 2*sqrt(5)

y = 4.4721359

As an exact value, EC is sqrt(20) or 2*sqrt(5) cm long.

As an approximate value, EC is roughly 4.4721359 cm long.

I would ask your teacher if you should use the exact or approximate value.

the answer is 13 cm