Quant Boosters - Geometry - Raman Sharma - Set 2
Q9) Two of the sides of a triangle are in the ratio 3:4. The medians to these sides are perpendicular to each other. If the third side of the triangle is 12root(5), find the smaller of the first two sides of the triangle.
Q10) The shortest median of a right-angled triangle is 25 units. If the area of the triangle is 336 sq.units, what is the length (in units) of the longest median of the triangle?
Q11) In triangle ABC, two lines DE and FG are drawn parallel to BC such that they divide AC in the ratio 2:3:5. Find the ratio of area of triangle ABC to area of the trapezium DEGF.
[OA: 100 : 21]
Q12) The parallel sides of Trapezium is 6 and 8 units respectively. Find the length of the line segment parallel to these sides and which divides the area of trapezium in equal halves.
A. 4 √3
B. 5 √ 2
[OA: Option b]
credits : @swetabh_kumar
let length be x..so 1/2 * (6x) * h1= 1/2 * (1/2 * 14 * h2)..h1 is the height of the smaller trapezium...h2 is overall heght.
now the line of legth x is divided into length 6 and 2 equal corner segments of legth (x-6)/2 each.
by similar triangles, h1/h2= (x-6)/2.
plug in the 1st eqn7/(6+x)=(x-6)/2
x^2 - 36 = 14
x = 5 root 2
Q13) What is the ratio of area of a regular dodecagon (a polygon with 12 sides) to the area of a regular hexagon if both the polygons are inscribed in the same circle?
[OA: 2 : √3]
Q14) In a triangle ABC AB = AC and angle BAC = 100°. AB is produced to D such that AD = BC. find angle BCD.
Q15) There are 7 smaller squares inside the large rectangle. If the green square has side length 1 and the brown square has side length 2, what is the area of the rectangle?
Q16) Let ABCDE be a regular pentagon. Construct an equilateral triangle PAB with point P inside the pentagon. Find the measure of the angle PCE.
Q17) QR = ?
Hint: Use Appollonius Theorem
PQ^2 + PR^2 = 2 * (x^2+279)
=>2 x^2 = 576 + 144 - 558
=>x = 9
QR = 2x = 18
Q18) A, B and C are the vertices of a triangle of area 60 cm^2. Let AD be the median drawn from vertex A to side BC and BY be the median from vertex B to AD. If BY is extended to meet AC at E, what is the area of triangle AYE?
[OA : 5 cm^2]
Q19) A circle is drawn such that its diameter coincides with the median BD of an equilateral triangle ABC of side length (4/ rt3) cm as shown in the picture. Find the area of the triangle ABC outside the circle.
OA : (π√3 - 2π)/6
Q20) The semi perimeter of a right angled triangle is 126cm and shortest median is 53cm.what is the area of the triangle which has the largest median as its longest side?
[OA : 1260 cm^2]
Q21) In a triangle ABC, median AM is drawn such that it divides ∠BAC in the ratio 1:2. AM is extended to D such that ∠ABD = 90. Given AC = 12 cm Find AD.
[OA: 24 cm]