# Quant Boosters - Geometry - Raman Sharma - Set 2

• Q26) Two sides of triangle are 10cm and 5cm in length and the length of the median to the third side is 13/2 cm.The area of the triangle is 6√x cm. Then find the value of x.

[OA: 14 cm]

• 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 • • @gaurav_sharma • @raman_sharma

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

63

61

44

61

54

61

43

61