In a triangle ABC, `a = 7, b = 8, c = 9, BD` is the median and BE the altitude from the vertex B. Match the following lists
`{:(a. BD =,p. 2),(b. BE =,q. 7),(c. ED =,r. sqrt45),(d. AE =,s. 6):}`

Options

A. a)`{:(a,b,c,d),(p,r,q,q):}`
B. b)
`{:(a,b,c,d),(r,q,s,p):}`
C. c)`{:(a,b,c,d),(q,r,p,s):}`
D. d)`{:(a,b,c,d),(s,p,q,r):}`

Answer

C

Explanation

In `DeltaABD`, using Cosine Rule
`cos A = (4^(2) + 9^(2) - BD^(2))/(2 xx 4 xx 9)`
In `DeltaABC`, Using Cosine Rule
`cos A = (8^(2) + 9^(2) - 7^(2))/(2 xx 8 xx 9)`
`rArr BD^(2) = 49`
`rArr BD = 7`
`DeltaBCD` is isosceles
`rArr ED = CD//2 = 2`
`BE = sqrt(7^(2) - 2^(2)) = sqrt45`
`AE = 6`