Question

please answer me step by step l know what is the answer​

Answer 1

Answer:

AE = 15.

DE = 8.

DC = 18.

Step-by-step explanation:

Take a look at AEBC.

∠A = ∠B  = ∠E = 90°

Since AEBC has four sides, we know it is a quadrilateral.

The sum of all four sides of a quadrilaterial is 360°, and we already know three angles.

Therefore, ∠A + ∠E + ∠B + ∠C = 360°.

⇒ 90° + 90° + 90° + ∠C = 360°.

⇒ ∠C = 90°.

∵ All four angles are 90°, and adjacent sides are not equal,

AEBC is a rectangle.

We know that opposite sides in a rectangle are equal,

⇒ AE = BC = 15.

⇒ AB = EC = 10.

Now, consider ADE.

We know that DEC is a straight line.

∠DEC = 180°.

∠DEC = ∠DEA + ∠AEC

180° = 90° + ∠DEA

⇒ ∠DEA = 90°.

∵ ∠DEA = 90°, ADE is a right angled triangle, with ∠E equaling 90°.

Now, we know the values of AD and AE, and we can find the value of DE by using the Pythagorean theorem since we have established that ADE is a right angle triangle.

By Using Pythagorean Theorem,

$AD^{2} = AE^{2} + DE^{2}$

$17^{2} = 15^{2} + DE ^{2}$

$289 = 225 + DE^2$

$DE^2 = 64$

Taking square root on both sides, $DE = 8.$

(DE cannot be - 8 as side lengths cannot be negative.)

Since we know the lengths of DE and EC, we can find DC.

DE + EC = DEC.

8 + 10 = 18.