A geometry problem by Luna Biswas

Geometry Level 3

Let ABC be an isosceles triangle where AB=AC and angle A measures 45 degrees.Length of BC is 10 cm.Find the area of the triangle. Take sqrt(2)=1.414.


The answer is 60.4.

Luna Biswas by Luna Biswas , 46, India

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1 solution

Luna Biswas
Aug 20, 2014

HINT Draw a line segment from C to AB intersecting at D such that AD=AB.Then find area by Heron's formula

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I guess you misunderstood the question madam.. Taking BC as the base of the triangle, which is equal to 10 cm, we have AB=AC=(5/cos 67.5)=13.. Using Heron's formula, given 3 sides as 13, 13 and 10, we can have the area of the triangle as 60.35.. I can see clearly that the way it has been solved by you is a way mistaken..

Mark Vincent Mamigo - 6 years, 7 months ago

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I have updated the answer to 60.4.

Note that you can find the height of the triangle as 5 tan ⁡ 67. 5 ∘ 5 \tan 67.5 ^ \circ , and hence the area is 5 × 5 × tan ⁡ 67. 5 ∘ ≈ 60.4 5 \times 5 \times \tan 67.5 ^ \circ \approx 60.4 .

Calvin Lin Staff - 6 years, 6 months ago

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