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# ABC above is an isosceles triangle in which AB = AC. What is the area

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Math Expert
Joined: 02 Sep 2009
Posts: 59712
ABC above is an isosceles triangle in which AB = AC. What is the area  [#permalink]

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13 Mar 2019, 01:31
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Difficulty:

15% (low)

Question Stats:

84% (00:52) correct 16% (01:07) wrong based on 43 sessions

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△ABC above is an isosceles triangle in which AB = AC. What is the area of △ABC?

A. 30
B. 24
C. 20
D. 15
E. 12

Attachment:

trid22 (1).png [ 8.33 KiB | Viewed 583 times ]

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Re: ABC above is an isosceles triangle in which AB = AC. What is the area  [#permalink]

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13 Mar 2019, 01:40
Using the formula:
{b(4a^2-b^2)^1/2}/4 = 12
B is the base or unequal side and a is the length of equal sides

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Re: ABC above is an isosceles triangle in which AB = AC. What is the area  [#permalink]

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13 Mar 2019, 03:38
Bunuel wrote:

△ABC above is an isosceles triangle in which AB = AC. What is the area of △ABC?

A. 30
B. 24
C. 20
D. 15
E. 12

Attachment:
trid22 (1).png

drop a perpendicular from A to BC D ; BD=DC= 3
so triangle ABD ; AD= 4 and area = 4*3*.5 = 6 and for complete triangel area = 12
IMO E
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Re: ABC above is an isosceles triangle in which AB = AC. What is the area  [#permalink]

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13 Mar 2019, 04:01
IMO E

perpendular from A will bisect the side BC

so we can find height by using pythagoras theoram.

√25 - 9 = √16 = 4

so area = 6*4/2 = 12

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Re: ABC above is an isosceles triangle in which AB = AC. What is the area  [#permalink]

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18 Mar 2019, 07:51
Bunuel wrote:

△ABC above is an isosceles triangle in which AB = AC. What is the area of △ABC?

A. 30
B. 24
C. 20
D. 15
E. 12

Attachment:
trid22 (1).png

Dropping a height from A to BC, we see that we have created two 3-4-5 right triangles, and so the height is 4.

Thus, the area is (4 x 6)/2 = 12.

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Re: ABC above is an isosceles triangle in which AB = AC. What is the area   [#permalink] 18 Mar 2019, 07:51
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