Question:
The area of a rectangle is 48 cm$^2$, and its perimeter is 28 cm. What is the length of the rectangle?
The area of a rectangle is 48 cm$^2$, and its perimeter is 28 cm. What is the length of the rectangle?
Show Hint
Form a quadratic equation using area and perimeter to find rectangle dimensions.
Updated On: Jul 29, 2025
- 6 cm
- 8 cm
- 10 cm
- 12 cm
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
- Step 1: Let length = $l$, breadth = $b$. Given: $lb = 48$, $2(l + b) = 28 \implies l + b = 14$.
- Step 2: Solve: $b = 14 - l$, substitute in $lb = 48$: $l(14 - l) = 48 \implies 14l - l^2 = 48 \implies l^2 - 14l + 48 = 0$.
- Step 3: Solve quadratic: $l = \frac{14 \pm \sqrt{196 - 192}}{2} = \frac{14 \pm 2}{2}$, so $l = 8$ or $l = 6$.
- Step 4: If $l = 8$, $b = 14 - 8 = 6$. Area = $8 \times 6 = 48$, perimeter = $2(8 + 6) = 28$. Matches.
- Step 5: If $l = 6$, $b = 8$, same result. Since length $\geq$ breadth, take $l = 8$.
- Step 6: Option (2) is 8 cm, correct.
- Step 2: Solve: $b = 14 - l$, substitute in $lb = 48$: $l(14 - l) = 48 \implies 14l - l^2 = 48 \implies l^2 - 14l + 48 = 0$.
- Step 3: Solve quadratic: $l = \frac{14 \pm \sqrt{196 - 192}}{2} = \frac{14 \pm 2}{2}$, so $l = 8$ or $l = 6$.
- Step 4: If $l = 8$, $b = 14 - 8 = 6$. Area = $8 \times 6 = 48$, perimeter = $2(8 + 6) = 28$. Matches.
- Step 5: If $l = 6$, $b = 8$, same result. Since length $\geq$ breadth, take $l = 8$.
- Step 6: Option (2) is 8 cm, correct.
Was this answer helpful?
0
0
Top Questions on Geometry
- A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting, and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?
- If \( A(2, 3) \) and \( B(4, 5) \) are the end points of a straight line AB, then the slope of straight line AB is:
- Spheres of unit diameter are centered at \( (l, m, n) \), where \( l, m, \) and \( n \) take every possible integer value. The distance between two spheres is computed from the center of one sphere to the center of another sphere. For a given sphere, \( x \) is the distance to its nearest sphere and \( y \) is the distance to its next nearest sphere. The value of \( \frac{y}{x} \) is:
In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and the line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?
Note: The figure shown is representative
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.
View More Questions
Questions Asked in CAT exam
- When 3333 is divided by 11, the remainder is
- CAT - 2024
- Divisibility and Remainder
- Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
- CAT - 2024
- Para Jumbles
- The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Scientific research shows that many animals are very intelligent and have sensory and motor abilities that dwarf ours. Dogs are able to detect diseases such as cancer and diabetes and warn humans of impending heart attacks and strokes. Elephants, whales, hippopotamuses, giraffes, and alligators use low-frequency sounds to communicate over long distances, often miles. Many animals also display wide-ranging emotions, including joy, happiness, empathy, compassion, grief, and even resentment and embarrassment. It’s not surprising that animals share many emotions with us because we also share brain structures, located in the limbic system, that are the seat of our emotions.- CAT - 2024
- Para Summary
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Taken outside the village of Trang Bang on June 8, 1972, the picture captured the trauma and indiscriminate violence of a conflict that claimed, by some estimates, a million or more civilian lives.
Paragraph: The horrifying photograph of children fleeing a deadly napalm attack has become a defining image not only of the Vietnam War but the 20th century. Dark smoke billowing behind them, the young subjects' faces are painted with a mixture of terror, pain and confusion. (2) Soldiers from the South Vietnamese army's 25th Division follow helplessly behind. (3) The picture was officially titled "The Terror of War," but the photo is better known by the nickname given to naked 9-year-old at its centre "Napalm Girl". (4)- CAT - 2024
- Para Completion
- Five jumbled up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
- CAT - 2024
- Para Jumbles
View More Questions