A 2 min read

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:

Source	OGQR 2020
Type	Problem Solving
Topic	Geometry
Sub-Topic	Triangle
Difficulty	Medium

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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