AP EAMCET · Maths · Application of Derivatives
If the area of a right angled triangle with hypotenuse 5 is maximum, then its perimeter is
- A \(12\)
- B \(2 \sqrt{3}+\sqrt{13}+5\)
- C \(7+\sqrt{21}\)
- D \(5(\sqrt{2}+1)\)
Answer & Solution
Correct Answer
(D) \(5(\sqrt{2}+1)\)
Step-by-step Solution
Detailed explanation
\(a^2+b^2=5^2\) Max area when \(a=b\): \(a^2+a^2=25 \Rightarrow 2a^2=25 \Rightarrow a=\frac{5}{\sqrt{2}}=\frac{5\sqrt{2}}{2}\) Perimeter \(P = a+b+c = \frac{5\sqrt{2}}{2}+\frac{5\sqrt{2}}{2}+5\) \(P = 5\sqrt{2}+5 = 5(\sqrt{2}+1)\)
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
- If \(\left(1+2 x+3 x^2\right)^{10}\) \(=a_0+a_1 x+a_2 x^2+\ldots+a_{20} x^{20}\)
then \(\frac{a_2}{a_1}\) is equal toAP EAMCET 2010 Medium - The mean deviation about the mean for the following data is
Class Interval \(0\)–\(2\) \(2\)–\(4\) \(4\)–\(6\) \(6\)–\(8\) \(8\)–\(10\) Frequency \(1\) \(3\) \(4\) \(1\) \(2\) AP EAMCET 2025 Medium - If \(\left(\mathrm{l}_1, \mathrm{~m}_1, \mathrm{n}_1\right),\left(\mathrm{l}_2, \mathrm{~m}_2, \mathrm{n}_2\right)\) are the direction cosines of two lines, then \(\left(1_1 m_2-1_2 m_1\right)^2+\left(m_1 n_2-m_2 n_1\right)^2+\) \(\left(\mathrm{n}_1 \mathrm{l}_2-\mathrm{n}_2 \mathrm{l}_1\right)^2+\left(\mathrm{l}_1 \mathrm{l}_2+\mathrm{m}_1 \mathrm{~m}_2+\mathrm{n}_1 \mathrm{n}_2\right)^2=\)AP EAMCET 2023 Hard
- The perpendicular distance from the point \((-1,1,0)\) to the line joining the points \((0,2,4)\) and \((3,0,1)\) isAP EAMCET 2024 Medium
- If the curves \(2 x^2+k y^2=30\) and \(3 y^2=28 x\) cut each other orthogonally, then \(k=\)AP EAMCET 2024 Easy
- The equation of the plane passing through and parallel to the vectors and isAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- If ambient temperature is 300 K , the rate of cooling at 600 K ts H . In the same surroundings, the rate of cooling at 900 K isAP EAMCET 2024 Medium
- Let \(A\) be a \(2 \times 2\) matrix with real entries. Let \(I\) be the \(2 \times 2\) identity matrix. \(\operatorname{Tr}(A)\) denotes the sum of diagonal entries of \(A\). Assume that \(A^2=I\)
Statement I If \(A \neq I\) and \(A \neq-1\), then \(\operatorname{det} A=-1\)
Statement II If \(A \neq I\) and \(A \neq-1\), then \(\operatorname{Tr} A \neq 0\)AP EAMCET 2021 Easy - If \(\left|\begin{array}{cc}x^3+2 x^2+3 x-2 & x^2+2 x+4 \\ x^3-x^2-2 x-1 & 3 x^3-2 x^2+4 x-2\end{array}\right|\) \(=a x^6+b x^5+c x^4+d x^3+e x^2+f x+g\), then \(a+b+c+d+e+f\) is equal toAP EAMCET 2021 Easy
- \(\frac{1+\tanh \frac{x}{2}}{1-\tanh \frac{x}{2}}\) is equal toAP EAMCET 2008 Medium
- A transmitting antenna of height \(20 \mathrm{~m}\) and the receiving antenna of height \(h\) are separated by a distance of \(40 \mathrm{~km}\) for satisfactory communication in line of sight (Los) mode. Then the value of \(h\) is (Give, radius of earth is \(6400 \mathrm{~km}\).)AP EAMCET 2019 Easy
- Potential difference between the points \(P\) and \(Q\) in the circuit shown is
AP EAMCET 2020 Easy