Quant Boosters  Geometry  Raman Sharma  Set 2

Q27) A triangle has sides of length √13, √17, and 2√5. Compute the area of the triangle

(Credits : Shubham Sharma)

Q28) ABC is an equilateral triangle with side length 7. BP = 3 , CP = 5 . What is the length AP ?
[OA: 8]

AC * BP + AB * CP = AP * BC
7 * 3 + 7 * 5 = 7 * AP
AP = 8
(ptlomy's theorem)
(credits : Varun Kumar Mandal)

Q26) In a ∆ PQR, PQ=QR , angle PQR = 90° and S and T are points on PR such that PS^2 + TR^2 = ST^2 then angle SQT = ?
a. 30
b. 45
c. 60
d. 75[OA : 45]


Q27) In a ∆ABC, ∆ = 6 , abc = 60, r = 1, then 1/a + 1/b + 1/c = ?
[OA: 47/60]

Q28) There is a square ABCD. There is a point P inside this square such that PA = 4, PB = 1, PD = 5. Find area of the square.
[OA : 17]

(credits : Anil Sharma)

Q29) In a ∆ABC , if tanA and tanB are the roots of the of pq(x²+1) = r²x. Then ∆ABC is
a. Right angled
b. Obtuse angled
c. Equilateral
d. Acute angled

pqx^2  r^2x + pq = 0
tanA + tanB = r^2/pq
tanA * tanB = 1
tan(A + B) = tan 90
so A + B = 90, so C = 90
So right angle

Q30) Given AB = AC. Find the measure of angle BAD



r= delta/s s=6 => a+b+c =12 , abc=60
a=3, b=4,c=5
1/a+1/b+1/c=47/60

@raman_sharma How the the length of side BE was computated?

@raman_sharma What is 'y' in your calculation of areas of the triangle? What formula have you used for calculating the area?

@raman_sharma
solution please