Question
A card is drawn from a standard deck of 52 cards. What
is the probability that it is a face card or a heart?Solution
ATQ, Face cards = 12 (J,Q,K of 4 suits) Hearts = 13 Overlap (face cards that are hearts) = J♥, Q♥, K♥ = 3 Favourable = 12 + 13 - 3 = 22 Probability = 22/52 = 11/26
- The base of a right pyramid is an equilateral triangle with side 12 cm. If the height of the pyramid is 40√3 cm, calculate the volume of the pyramid.
What is the height of an equilateral triangle if each side measures 8√3 cm?
A triangle has sides 13 cm, 14 cm, and 15 cm. What is the radius of its incircle?
What is the height of an equilateral triangle with a side length of 10√2 cm?
If perpendicular and base of a right-angle triangle is, 18 cm and 24 cm, respectively, then find the length of the shortest median of triangle.
- In triangle GHI, JK is drawn parallel to side HI. If GJ = 7 cm, JH = 2 cm, and GK = 14 cm, find GI.
In ΔPQR, PQ = 4 cm, QR = 3 cm, and RP = 3.5 cm. ΔDEF is similar to ΔPQR. If EF = 9 cm, what is the perimeter of ΔDEF?
- If the perpendicular from a vertex of an equilateral triangle to the opposite side is 15√3 cm, find its inradius.
An equilateral triangle has all sides of length 14√3 cm. What is the altitude of this triangle?
The ratio of the height to the base of a triangle is 3:2. If the sum of the height and base of the triangle is 25 cm, what is the area of the triangle?
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