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:
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.
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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