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3. In rhombus ABCD, AE = 5 and BE = 12 Find the length of AB and the perimeter of ABCD.

3. In rhombus ABCD, AE = 5 and BE = 12 Find the length of AB and the perimeter of-example-1
User Spoeken
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1 Answer

5 votes

Assuming number 2 is related,

Let's identify first AngleEBA since AngleEAB = 38 Degrees

Let,

x = AngleEAB = AngleEAD = AngleECD = AngleECB; 4x since the angles are equal

y = AngleEBA = AngleEBC = AngleEDC = AngleEDA; 4y since the angles are equal

Sum of all angles inside the Rhombus = 360 Degrees

We get,

(AngleABE x 4) + (AngleEAB x 4) = 360 Degrees.

4x + 4y = 360

4x + 4(38) = 360

4x = 360 - 152

x = AngleEBA = 52 Degrees

Let's identify AngleAEB:

AngleAEB = 180 - (AngleEAB + AngleEBA) = 180 - (38 + 52)

AngleAEB = 90 Degrees

It's a right triangle,

thus, we could apply the Pythagorean theorem to get the length of AB.

Let, a = 5; b = 12; c = AB

a^2 + b^2 = c^2

(5)^2 + (12)^2 = c^2

25 + 144 = c^2

c = Square root of 169

c = AB = 13

Since the rhombus is a square, all sides are equal.

Perimeter of ABCD = 4s

Perimeter of ABCD = 4 x 13

Perimeter of ABCD = 52

User Ferdil
by
3.2k points