Question:
A rectangle with the largest possible area is inscribed in a semi-circle. Find the ratio of the larger side to the smaller side.
A rectangle with the largest possible area is inscribed in a semi-circle. Find the ratio of the larger side to the smaller side.
Updated On: May 17, 2024
Hide Solution
Verified By Collegedunia
Solution and Explanation
The correct answer is: 2:1.
There are no critical points in the feasible domain.
Since there are no critical points, we need to consider the boundary points.
Now \((\frac{l}{2})^2=b^2=>I=2b\)
\(\frac{l}{2}=\frac{2}{1}\)
Therefore, the ratio of the larger side to the smaller side of the rectangle with the largest possible area inscribed in a semi-circle is 2:1.
There are no critical points in the feasible domain.
Since there are no critical points, we need to consider the boundary points.
Now \((\frac{l}{2})^2=b^2=>I=2b\)
\(\frac{l}{2}=\frac{2}{1}\)
Therefore, the ratio of the larger side to the smaller side of the rectangle with the largest possible area inscribed in a semi-circle is 2:1.
Was this answer helpful?
1
4
Top Questions on Triangles, Circles & Quadrilaterals
- ABC is a triangle with BC = 5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE = 3. The value of AB2-AE2+6CD is:
- XAT - 2023
- Quantitative Ability and Data Interpretation
- Triangles, Circles & Quadrilaterals
- ABC is a triangle and the coordinates of A, B, and C are (a, b - 2c), (a, b + 4c), and (-2a, 3c), respectively, where a, b, and c are positive numbers. The area of the triangle ABC is:
- XAT - 2023
- Quantitative Ability and Data Interpretation
- Triangles, Circles & Quadrilaterals
ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB . Kindly note that BC<AD . P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC . If the area of the triangle CPD is 4√3. Find the area of the triangle ABQ.
- XAT - 2023
- Quantitative Ability and Data Interpretation
- Triangles, Circles & Quadrilaterals
- Let \(ΔABC\) be an isosceles triangle such that \(AB\) and \(AC\) are of equal length. \(AD\) is the altitude from \(A\) on \(BC\) and \(BE\) is the altitude from \(B\) on \(AC\) . If \(AD\) and \(BE\) intersect at \(O\) such that \(∠AOB =105\degree\) , then \(\frac{AD}{BE}\) equals
- CAT - 2023
- Quantitative Aptitude
- Triangles, Circles & Quadrilaterals
- A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is
- CAT - 2023
- Quantitative Aptitude
- Triangles, Circles & Quadrilaterals
View More Questions
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- If $(a + b\sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a + b + n)$ is ?
- CAT - 2024
- Algebra
- A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
- CAT - 2024
- Mensuration
- Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
- Algebra
View More Questions