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XAT 2023 — QA & DI Question 4

TrianglesEasy

ABC is a triangle with BC = 5. D is thefoot of the perpendicular from A on BC. E is a point on CD such that BE = 3. 

The value of AB2 - AE2 + 6CD is:

Answer & solution

  • A

    5

  • B

    10

  • C

    14

  • D

    18

  • 21

Solution

​​​​​​​

Given, BC = 5 and BE = 3

In â–³ABD ⇒ AB2 = AD2 + BD2    ...(1)
In â–³AED ⇒ AE2 = AD2 + DE2    ...(2)

(1) - (2) 
⇒ AB2 - AE2 = BD2 - DE2 
⇒ AB2 - AE2 = x2 - (3 - x)2 
⇒ AB2 - AE2 = x2 - 9 - x2 + 6x 
⇒ AB2 - AE2 = - 9 + 6x 

We need to find AB2 - AE2 + 6CD
= (-9 + 6x) + 6 × (5 - x)
= -9 + 6x + 30 - 6x
= 21

Hence, option (e).

XAT 2023 QA & DI Q4: ABC is a triangle with BC = 5. D is thefoot of the perpendicular from A on BC. E is a point on CD such that BE — Solution | TheCATExam