KCET · Maths · Application of Derivatives
The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm , then
- A Breadth \(\leq 15 \mathrm{~cm}\)
- B Breadth \(\geq 15 \mathrm{~cm}\)
- C Length \(\leq 15 \mathrm{~cm}\)
- D Length \(=15 \mathrm{~cm}\)
Answer & Solution
Correct Answer
(B) Breadth \(\geq 15 \mathrm{~cm}\)
Step-by-step Solution
Detailed explanation
Since, perimeter \(\geq 180\)
\(\Rightarrow 2\) (length + breadth) \(\geq 180\)
\(\Rightarrow 5\) breadth + breadth \(\geq 90\)
\([\because\) length \(=5\) breadth \(]\)
\(\Rightarrow 6\) breadth \(\geq 90\)
Hence, breadth \(\geq 15\)
\(\Rightarrow 2\) (length + breadth) \(\geq 180\)
\(\Rightarrow 5\) breadth + breadth \(\geq 90\)
\([\because\) length \(=5\) breadth \(]\)
\(\Rightarrow 6\) breadth \(\geq 90\)
Hence, breadth \(\geq 15\)
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 \( y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \), then \( \frac{d y}{d x} \) at \( x=1 \) isKCET 2014 Easy
- Consider the following statements Statement 1 : \(\lim _{x \rightarrow 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a}\) is 1 (where \(a+b+c \neq 0\) ).
Statement \(2: \lim _{x \rightarrow 2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2}\) is \(\frac{1}{4}\).KCET 2021 Medium - If the area of the auxillary circle of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b)\) is twice the area of the ellipse, then the eccentricity of the ellipse isKCET 2007 Easy
- If there are two values of ' \(a\) ' which makes determinant
\[
\Delta=\left|\begin{array}{ccc}
1 & -2 & 5 \\
2 & a & -1 \\
0 & 4 & 2 a
\end{array}\right|=86
\]
Then, the sum of these number isKCET 2022 Medium - If \(\alpha\) is a complex number such that \(\alpha^{2}-\alpha+1=0\), then \(\alpha^{2011}\) is equal toKCET 2012 Hard
- The total number of terms in the expansion of \( (x+a)^{47}-(x-a)^{47} \) after simplification isKCET 2017 Easy
More PYQs from KCET
- \( \int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x \) isKCET 2015 Easy
- The sine of the angle between the straight line \(\frac{x-2}{3}=\frac{3-y}{-4}=\frac{z-4}{5}\) and the plane \(2 x-2 y+z=5\) isKCET 2020 Easy
- A radioactive sample \(S_{1}\) having the activity \(\mathrm{A}_{1}\) has twice the number of nuclei as another sample \(S_{2}\) of activity \(A_{2}\). If \(A_{2}=2 A_{1}\), then the ratio of half-life of \(S_{1}\) to the half-life of \(S_{2}\) isKCET 2010 Medium
- Biologically active adrenaline and ephedrine used to increase blood pressure containKCET 2024 Hard
- Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls when in air,KCET 2017 Easy
- If \( \alpha \) and \( \beta \) are roots of the equation \( \chi^{2}+x+1=0 \) then \( \alpha^{2}+\beta^{2} \) isKCET 2019 Medium