Question:
The length of a rectangle is increased to \(\frac{3}{2} \) times of its length and breadth is reduced to \(\frac{1}{3}rd\) of its breadth. What is the change in area?
The length of a rectangle is increased to \(\frac{3}{2} \) times of its length and breadth is reduced to \(\frac{1}{3}rd\) of its breadth. What is the change in area?
Updated On: Oct 10, 2024
- \(\frac{1}{3}\)
- \(\frac{1}{4}\)
- \(\frac{1}{2}\)
- No Change
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Let the length of previous rectangle be L.
Then the length of new rectangle = \(\frac{3}{2}\)L.
Let the breadth of previous rectangle be B.
Then new breadth of rectangle =\(\frac{2}{3}\)B.
Now, previous area of rectangle = LB
and the new area = \(\frac{3}{2}\)L × \(\frac{2}{3}\)B = LB
There would be no any change in area of rectangle
So the correct option is (D)
Then the length of new rectangle = \(\frac{3}{2}\)L.
Let the breadth of previous rectangle be B.
Then new breadth of rectangle =\(\frac{2}{3}\)B.
Now, previous area of rectangle = LB
and the new area = \(\frac{3}{2}\)L × \(\frac{2}{3}\)B = LB
There would be no any change in area of rectangle
So the correct option is (D)
Was this answer helpful?
0
0
Top Questions on Geometry
- Consider a right-angled triangle ABC, right angled at B. Two circles, each of radius r, are drawn inside the triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The two circles also touch each other (see the image below).
If AB = 18 cm and BC = 24 cm, then find the value of r.
- A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per second, and the ball always moves on straight lines along the ground.
Consider the following two additional pieces of information:
I. The dimension of the ground is 80 metres × 50 metres.
II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres.
Consider the problem of computing the following: how many seconds does it take for Raju to get the ball back since he passed it to Rivu? Choose the correct option. - A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long and the other two sides are equal. The perpendicular distance, from the corner of the plot, where the two equal sides meet, to the base, is 200 feet.
To counter the adverse effect of climate change, the farmer wants to dig a circular pond. He plans that half of the circular area will be inside the triangular plot and the other half will be outside, which he will purchase at the market rate from his neighbour. The diameter of the circular plot is entirely contained in the base and the circumference of the pond touches the two equal sides of the triangle from inside.
If the market rate per square feet of land is Rs. 1400, how much does the farmer must pay to buy the land from his neighbour for the pond? (Choose the closest option.) - A rectangle \(ABCD\) has sides \(AB = 45 \, \text{cm}\) and \(BC = 26 \, \text{cm}\). Point \(E\) is the midpoint of side \(CD\). Find the radius of the incircle of the triangle \(\triangle AED\).
- PQR is a triangle. The bisectors of the internal angle ∠Q and external angle ∠R intersect at M. If ∠QMR = 40°, then ∠P is:
View More Questions
Questions Asked in MAT exam
- In the following sentence, a part of the sentence is underlined. Beneath each sentence four different ways of phrasing the underlined part are indicated. Choose the best alternative among the four options.
There \(\underline {\text{have}\ \text{been}\ \text{heavy}\ \text{rainfall}}\) yesterday- MAT - 2018
- Sentence Correction
- Who among the following cannot be impeached?
- MAT - 2018
- Politics and Government
- Who is leading the LTTE delegation for the peace process with Sri Lanka?
- MAT - 2018
- International Organizations
- Who was the first UN Secretary General?
- MAT - 2018
- Politics and Government
- Which of the following sources yields the maximum revenue to the Union Government?
- MAT - 2018
- Politics and Government
View More Questions