Question
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. find the dimensions of the garden.
✓
Answer
Let the dimensions (i.e., length and width) of the garden be x and y m respectively.
Then, x = y + 4 and $\frac{1}{2}$(2x + 2y) = 36
$\Rightarrow$ x - y = 4 ...(1)
x + y = 36 ...(2)
Let us draw the graphs of equations (1) and (2) by finding two solutions for each of the equations. These two solution of the equations (1) and (2) are given below in table 1 and table 2 respectively.
For equation (1)
x - y = 4
$\Rightarrow$ y = x - 4
Table 1 of solutions
| x | 4 | 2 |
| y | 0 | -2 |
$\Rightarrow$ y = 36 - x
Table 2 of solutions
| x | 20 | 16 |
| y | 16 | 20 |
Also, we plot the points C(20, 16) and D(16, 20) on the same graph paper and join these points to form the line CD representing the equation (2) as shown in the same figure.
In the figure, we observe that the two lines intersect at the point C(20, 16) So x = 20, y = 16 is the required solution of the pair of linear equations formed. i.e., the dimensions of the garden are 20 m and 16 m.
Verification : substituting x = 20 and y = 16 in (1) and (2), we find that both the equations are satisfied as shown below:
20 - 16 = 4
20 + 16 = 36
This verifies the solution.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the roots of the following equations, if they exist, by applying the quadratic formula:
$x^2 - 2ax - (4b^2 - a^2) = 0$
→$x^2 - 2ax - (4b^2 - a^2) = 0$
If $\sin\theta+\cos\theta=\text{x},$ prove that $\sin^6\theta+\cos^6\theta=\frac{4-3(\text{x}^2-1)^2}{4}.$
→From a point on the ground, the angles of elevation of the bottom and the top of a tower fixed at the top of a 20 m high building are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower.
→Solve the following systems of equations by using the method of cross multiplication:
$6x - 5y - 16 = 0,$
$7x - 13y + 10 = 0$
→$6x - 5y - 16 = 0,$
$7x - 13y + 10 = 0$
Find the missing frequency f1 and f2 in the following distribution table, if N = 100 and median is 32.
| Class: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | Total |
| Frequency: | 10 | F1 | 25 | 30 | F2 | 10 | 100 |
While covering a distance of 30km. Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit. Find their speeds of walking.
The angle of elevation of the top of an unifinished tower at a distance of 75m from its base is 30°. How much higher must the tower be raised so that the angle of elevation of its top at the same point may be 60°? $\big[\text{Take}\sqrt{3}=1.732\big]$
→Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is $7: 15$. Find the numbers.
→The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.