Quant Boosters - Geometry - Raman Sharma - Set 2


  • Faculty and Content Developer at TathaGat


    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.

    [OA: 36]


  • Faculty and Content Developer at TathaGat


    0_1507022284504_72d32eeb-7099-46f7-83c7-4c62c0d73eb9-image.png


  • Faculty and Content Developer at TathaGat


    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?

    [OA: 48.5]


  • Faculty and Content Developer at TathaGat


    0_1507022589502_1cf95aac-4514-4d5e-a276-0cf210e023dc-13781761_992876177496680_2726106952529985480_n.jpg


  • Faculty and Content Developer at TathaGat


    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]


  • Faculty and Content Developer at TathaGat


    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
    C. 7
    D. 7/√2

    [OA: Option b]


  • Faculty and Content Developer at TathaGat


    0_1507022873128_5d5ae6e7-88a6-403f-aa7d-ceb52fd2f8b9-12107268_835647809886185_7228629521719374536_n.jpg


  • Faculty and Content Developer at TathaGat


    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.
    so (6+x)h1=7h2
    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


  • Faculty and Content Developer at TathaGat


    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]


  • Faculty and Content Developer at TathaGat


    Q14) In a triangle ABC AB = AC and angle BAC = 100°. AB is produced to D such that AD = BC. find angle BCD.

    0_1507023001662_b34be995-0ba4-491c-9880-b670e13743f3-12243263_850941525023480_7604062874007029589_n.jpg

    [OA: 10]


  • Faculty and Content Developer at TathaGat


    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?

    0_1507023098227_7d6309ea-0a97-44de-9f49-7f47e8ca0855-13507198_979022148882083_1259985714960540843_n.jpg

    [OA: 63]


  • Faculty and Content Developer at TathaGat


    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.

    [OA: 6]


  • Faculty and Content Developer at TathaGat


    Q17) QR = ?

    0_1507023649129_5e563d29-64ef-4529-a45c-3ee0cef47420-20046307_1337438329707128_5854284451029036500_n.jpg

    [OA: 18]


  • Faculty and Content Developer at TathaGat


    Hint: Use Appollonius Theorem
    PQ^2 + PR^2 = 2 * (x^2+279)
    =>2 x^2 = 576 + 144 - 558
    =>x = 9
    QR = 2x = 18


  • Faculty and Content Developer at TathaGat


    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]


  • Faculty and Content Developer at TathaGat


    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.

    0_1486700769654_G_2_1.jpg

    OA : (π√3 - 2π)/6


  • Faculty and Content Developer at TathaGat


    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]


  • Faculty and Content Developer at TathaGat


    0_1486700848177_G_4_1.jpg


  • Faculty and Content Developer at TathaGat


    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]


  • Faculty and Content Developer at TathaGat


    0_1514351100391_7b6e6cb8-dc76-48b4-aa3e-3c47980a397a-image.png


 

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