Question
The length of three perpendicular distances of three
sides of an equilateral triangle from a point which lies inside that triangle are 9 cm, 8 cm and 7 cm respectively. What is the perimeter of the triangle?Solution
Let in ∆ABC, AB = BC = CA = a cm ON ⊥ AB OM ⊥ AC OP ⊥ BC Whose length respectively is ON = 9 cm, OM = 8 cm, OP = 7 cm. Area of ∆ABC = Area of ∆AOB + Area of ∆AOC + Area of ∆BOC √3/4 a² = 1/2 × ON × AB + 1/2 × OM × AC + 1/2 × OP × BC √3/4 a² = 1/2 × 9 × a + 1/2 × 8 × a + 1/2 × 7 × a √3/4 a² = 1/2a (9 + 8 + 7) √3/4 a² = 1/2 a × 24 √3/4 a² = 12 a a = (12 × 4)/√3 a = 4√3× 4 = 13√3 Side of ∆ABC, a = 16√3 ∴ Perimeter = 3 × 16√3 = 48√3
What approximate value should replace the question mark?
12.45% of 640.20 − 60% of 2500 = ? − 9000.10
`[(7.99)^2 - (13.001)^2 + (4.01)^3]^2=` ?
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
What value should come in place of question mark (?) in the following question. (You need not to calcualte the exact value)
?/647 = 226/ ?
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
A, B & C have Rs.1550 together. If they divide the money in the ratio 1:3:1 respectively. Find the difference of amount received by B and C.
What approximate value should come in the place of (?) in the following questions?
∛(92.8 + √1025) * ? = 16.06% of 750
√1024.21 × √624.89 ÷ 4.98 + 11.99 × 4.01 = ?
√784 × 3 + (713.99 ÷ 6.98) = ?% of 619.99
11.11% of (123.45 + 234.56) + 10.01³ - (5.05 of 7.07) = ? of (88.88 - 33.33)
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