Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2012MathematicsSequences and Series

In a triangle, the angle are in AP and the lengths of the two larger sides are 10 and 9 , respectively, then the length of the third side can be

Options

  1. A5 6
  2. B0.7
  3. C15- 6
  4. DNone of these

Correct answer

A. 5 6

Step-by-step solution

Let the angles be A=x-d, B=x, C=x+d , Then, x-d+x+x+d=180^ 3 x=180^ x=60^ Therefore, two larger angles are B and C . Hence, b=9 and c=10 . Now, array cc & B= c^2+a^2-b^2 2 a c & 1 2 = 100+a^2-81 20 a & a^2-10 a+19=0 & a=5 6 array

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Every term of a geometric progression is positive , and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is: 2026If k is the arithmetic mean of two given quantities and p, q are the geometric means between the same two quantities, then p^3 + q^3 is: 2026Let ' a ' and ' b ' be two numbers where a < b . The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 2 2026The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14. Find the numbers. 2026Let a₁, a₂, a₃, be a geometric progression of positive integers such that a₁ = 3 and a_ n+2 - 2a_n = a_ n+1 for all positive integers n . What is the value of a₁ + a₂ + a₃ + a₄ + a 2026The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is 2026If we insert two numbers between 2 and 4 so that the resulting sequence is in G.P, then the inserted numbers in the order are 2026If S _ n =1^3+2^3+ . .+ n ^3 and T _ n =1+2+ . .+ n , then 2025 Full Sequences and Series list All Manipal MET PYQs