Square and triangle

Question

In the figure, ABCD is a square and AED is the equilateral triangle. Which of the following is true about x?

10<=x<=20
20<=x<=30
30<=x<=40
40<=x<=50
50<=x<=60

jax91 · Answer

ABE and DEC are identical isosceles triangles.

<BAE is 30, which makes <BEA=75, similarly <DEC =75

So <BEC = 150 (360 - (75 + 75 + 60))

Since ABE and DEC are identical, BE = CE

Thus BEC is also an isosceles triangle.

x=(180-150)/2 = 15

IMO A

Mikko · Answer

jax91 <img src="{SMILIES_PATH}/080402cool_prv.gif" alt=":cool" title="Cool" />

bhushan252 · Answer

with equilateral triangle we can conclude following
AE = AD = ED with ang EAD = ang EDA = ang EAD = 60 deg
ang EDC = ang EAB = 30 deg..with ED = DC triangle EDC & EAB is isoselese triangle ang DEC = ang ECD = 75 deg
with ang BCD = 90 = ang BCE (x deg) + ang ECD (75 deg)....x = 15 deg ... OA A

Economist · Answer

How can we say that 'ABE and DEC are identical isosceles triangles' ? Just by looking at the given figure?

bhushan252 · Answer

no bcoz of equilateral triangle......ED = CD hence isoscelas

jax91 · Answer

The sqaure and the triangle share one common side (the base).

so from that we get AE=AB=DE=DC

Also <EAB=<EDC = 90-60 = 30

We get two side of the triangles equal and also the angle between them is equal. Thus they are identical. :-D

Square and triangle

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