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: Length 20 m, width 16 m.
Step-by-step solution
Idea: Half the perimeter of a rectangle is length + width. Together with “length = width + 4” this gives a pair of equations.
- Let length = l m and width = w m. Half the perimeter = l + w, so l + w = 36 … (1). Also l = w + 4 … (2).1 mark
- Substitute (2) in (1): w + 4 + w = 36 ⇒ 2w = 32 ⇒ w = 16.1 mark
- l = 16 + 4 = 20. The garden is 20 m long and 16 m wide.1 mark
Length 20 m, width 16 m.
Check: 20 + 16 = 36 ✓ and 20 − 16 = 4 ✓. Full perimeter 2 × 36 = 72 m.
Answer to write in the exam
Let length = l m, width = w m
l + w = 36 (half perimeter) … (1)
l = w + 4 … (2)
(2) in (1): 2w + 4 = 36 ⇒ w = 16
l = 20
∴ Length = 20 m, width = 16 m
Common mistakes that cost marks
- Writing 2(l + w) = 36: 36 m is half the perimeter, so l + w = 36.
- Writing w = l + 4 (width longer than length).
How this can come in the exam
MCQ (1 mark)
A rectangle’s perimeter is 50 cm and its length is 5 cm more than its breadth. Its length is
- 10 cm
- 15 cm
- 20 cm
- 12.5 cm
Show answer
(B) 15 cm
l + b = 25, l − b = 5 ⇒ l = 15.
Try one yourself
Half the perimeter of a rectangle is 28 cm and its length is three times its width. Find its sides.
Show answer
l + w = 28, l = 3w ⇒ w = 7 cm, l = 21 cm.
More questions like this
- Given the linear equation 2x + 3y − 8 = 0, write another linear equation in two variables so that the graphs of the pair formed represent (i) intersecting lines (ii) parallel lines (iii) coincident lines.
- Here is a problem that was posed by Mahāvīrāchārya in Gaṇita sāra saṅgraha (c. 850 CE).
The price of 9 citrons and 7 fragrant wood-apples taken together is 107; and the price of 7 citrons and 9 fragrant wood-apples taken together is 101.
O mathematician, tell me quickly the price of each citron and of each fragrant wood-apple.
(Hint: The given problem can be modelled as
9x + 7y = 107
7x + 9y = 101
Can you figure out a way of solving these equations without directly using elimination or the substitution method? What is special in this pair of equations? The x and y coefficients are interchanged in the 2 equations.
What will happen if we add the pair of equations? What will happen if we subtract the pair of equations? Can the resulting equations be solved to find the values of x and y?) - 5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of each pencil and pen.
- Find the height of the stool.
- The graph of the line y = 3x, passing through (0, 0) and (2, 6) is given below.
All Linear equations in two variables questions · All maths questions