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In the figure above, if triangles ABC, ACD, and ADE are isosceles right triangles and the area of ΔABC is 6, then the area of ΔADE is – OGQR 2020 Question #87 with Solution

OGQR 2020: Question No. 87

In the figure above, if triangles ABC, ACD, and ADE are isosceles right triangles and the area of ΔABC is 6, then the area of ΔADE is:

SourceOGQR 2020
TypeProblem Solving
TopicGeometry
Sub-TopicTriangle
DifficultyMedium

Solution

Given

In this question, we are given

  • A diagram consists of three triangles ABC, ACD, and ADE – all of them are individually isosceles right triangles.
  • The area of ΔABC is 6.

To Find

We need to determine

  • The area of ΔADE.

Approach & Working

Let us assume the length of AB = n

  • As ΔABC is an isosceles right angle triangle, AB = BC = n
  • Therefore, AC = √(n2 + n2) = √2n

We also know that ΔACD is an isosceles right angle triangle.

  • Hence, AC = CD = √2n
  • Therefore, AD = √(2n2 + 2n2) = 2n

Finally, ΔADE is an isosceles right-angle triangle.

  • Hence, AD = DE = 2n
  • Thus, the area of ΔADE = ½ * 2n * 2n = 2n2

We are also given that area of ΔABC is 6.

  • Hence, we can write = ½ * n * n = ½ n2 = 6
    • Or, n2 = 12
  • Therefore, area of ΔADE = 2n2 = 2 * 12 = 24

Hence, the correct answer is option B.

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