Question

(ii) The length of a rectangle is 6 m less than three times its breadth. The dimensions of the rectangle, if its perimeter is 148 m, are
(a) 54 m, 20 m
(b) 14 m, 40 m
( c) 54 m, 24 m
(d) 54 m, 14 m ​

Answer 1

Answer:

(a) 54 m, 20 m

Step-by-step explanation:

Given, L= 3B - 6

Perimeter = 2(L+ B) = 148m

⇒ L + B = 148/2 = 74

∴ 3B - 6 + B = 74

⇒ 4B = 80

⇒ B = 20m

∵ L = 3B -6 ⇒ 3×20 - 6

L = 60 - 6

L = 54 m

Answer 2

Option (a) is correct answer.

Here,

• Perimeter of rectangle = 148 m

Let the breadth of rectangle be n

then, its length will be 3n - 6

We know,

Perimeter of rectangle = 2{length+breadth}

$\large = > 2 \{(3n - 6) + (n) \} = 148 \\\large = > \: \: 2 \{ 3n - 6 + n\} = 148 \\\huge = > \: \: 2 \{4n - 6 \} = 148\\ \\ \huge = > \: \: \: 4n - 6 = \frac{148}{2} \\ \\ \huge = > \: \: \: 4n - 6 = 74 \\ \\ = >\huge \: \: \: \: \: \: \: 4n = 74 + 6 \\ \\ \huge = > \: \: \: \: \: \: 4n = 80 \\ \\ \huge = > \: \: \: \: \: \frac{4n}{4} = \frac{80}{4} \\ \\\huge = > \: \: \: \: \: \: n = 20$

Thus,

• Breadth of rectangle is 20 m
• Length of rectangle is 54 m