Question

in the figure angle ABC=angle ACD= angle ADC=90 degree. if AB=AC=CD=DE=1cm. find the length of AE

Answer 1

Answer:

ANSWER=2cm

solution is attached...

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Answer 2

Given,

In the given figure,

∠ABC = ∠ACD = ∠ADE = 90°, and,

AB = AC = CD = DE = 1 cm.

To find,

Length of AE.

Solution,

This problem can be simply solved by using the below process.

In the given problem, we need to find AE. This can be done by applying Pythagoras theorem in ΔADE.

Pythagoras' theorem states that, for a right-angled triangle,

$Hypotenuse^{2} =Base^{2} +Perpendicular^{2}$

Now, considering the ΔADE, since we know DE and ∠ADE = 90°, we need to find AD. To find AD, similarly, we should know AC.

Now, it can be seen that ΔABC is a right triangle for which, AB = BC = 1 cm and ∠ABC = 90°.

Applying Pythagoras theorem in ΔABC, we get,

AC² = AB² + BC²

⇒ AC² = 1² + 1²

⇒ AC = √2

We know AC, now applying Pythagoras theorem in ΔACD, so,

AD² = AC² + CD²

⇒ AD² = (√2)² + 1²

⇒ AD² = 2 + 1

⇒ AD = √3

Now, finally applying Pythagoras theorem in ΔADE, that is,

AE² = AD² + DE²

⇒ AE² = (√3)² + 1²

⇒ AE² = 3 + 1

⇒ AE = √4

⇒ AE = 2 cm.

Therefore, for the given figure, the length of AE will be 2 cm.