TS EAMCET · Maths · Properties of Triangles
If \(\mathrm{p}_1, \mathrm{p}_2, \mathrm{p}_3\) are the altitudes and \(a=4, b=5, c=6\) are the sides of a triangle ABC, then \(\frac{1}{\mathrm{p}_1{ }^2}+\frac{1}{\mathrm{p}_2{ }^2}+\frac{1}{\mathrm{p}_3{ }^2}=\)
- A \(\frac{77}{225}\)
- B \(\frac{44}{225}\)
- C \(\frac{308}{225}\)
- D \(\frac{22}{75}\)
Answer & Solution
Correct Answer
(B) \(\frac{44}{225}\)
Step-by-step Solution
Detailed explanation
\(s = \frac{a+b+c}{2} = \frac{4+5+6}{2} = \frac{15}{2}\) \(A^2 = s(s-a)(s-b)(s-c) = \frac{15}{2}(\frac{15}{2}-4)(\frac{15}{2}-5)(\frac{15}{2}-6)\) \(A^2 = \frac{15}{2} \cdot \frac{7}{2} \cdot \frac{5}{2} \cdot \frac{3}{2} = \frac{1575}{16}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \[ \lim _{x \rightarrow 2} \frac{x^3-x^2-x-2}{2 x^3-3 x^2-3 x+2}= \]TS EAMCET 2022 Easy
- If \(\int \frac{x^2\left(x \sec ^2 x+\tan x\right)}{(x \tan x+1)^2} d x=A \log\) \((|x \sin x+\cos x|)+B \frac{f(x)}{(x \tan x+1)}+C\), then \(f(A+B)=\)TS EAMCET 2020 Medium
- The locus of the mid-points of the chords of the circle \(x^2+y^2=16\) which are tangents to the hyperbola \(9 x^2-16 y^2=144\) isTS EAMCET 2018 Medium
- If is the normal form of the equation of a straight line and are respectively intercepts of this line, thenTS EAMCET 2019 Easy
- The circle \(4 x^2+4 y^2-12 x-12 y+9=0\)TS EAMCET 2013 Medium
- are altitudes of a triangle drawn from the vertices respectively. If is the area of the triangle and is the sum of the sides, thenTS EAMCET 2019 Easy
More PYQs from TS EAMCET
- If \(f\) is defined on \(\mathbb{R}\) such that \(f(\mathrm{x}) f(-\mathrm{x})=9\), then \(\int_{-23}^{23} \frac{d x}{3+f(x)}\)TS EAMCET 2023 Hard
- For the reaction is dissociated at a total pressure The correct relation between and isTS EAMCET 2021 Hard
- The maximum interval in which the slopes of the tangents drawn to the curve \(y=x^4+5 x^3+9 x^2+6 x+2\) increase isTS EAMCET 2024 Easy
- A charge of \(1 \mu \mathrm{C}\) is divided into two parts such that their charges are in the ratio of \(2: 3\). These two charges are kept at a distance \(1 \mathrm{~m}\) apart in vacuum. Then, the electric force between them \((\) in \(N)\) isTS EAMCET 2008 Easy
- If the point satisfies the equation , thenTS EAMCET 2022 Medium
- Composition of siderite ore isTS EAMCET 2025 Easy