Question

The length of a rectangular garden is
6 m more than thrice its breadth. If its
perimeter is 100 m, find the dimensions
of the garden.​

Answer 1

Answer:

This is your answer

Step-by-step explanation:

Let the width of the rectangle be b, then its length will be (3b+6).

2b+2(3b+6) = 100, or

2b +6b+ 12= 100, or

8b = 88, or

b =11

Length = 11*3+6 = 39 cm.

Length = 39 cm, width = 11 cm

Answer 2

Given:

• length of a rectangular garden is 6 m more than thrice its breadth.

• Perimeter = 100m

Let:

• Breadth of rectangular garden = x

• Length of rectangular garden = 6 + 3x

To find:

• Length

• Breadth

Solution:

So to find dimensions we should know value of x

We know:-

Perimeter of rectangle = 2 (Length + Breadth)

By using this formula we can find value of x

• Perimeter of rectangle = 2 (Length + Breadth)

• 100 = 2 (x + 6 + 3x)

• 100 = 2 ([x+3x] + 6)

• 100= 2(4x + 6)

• 100 = [2 × 4x] + [2 × 6]

• 100 = 8x + [2 × 6]

• 100 = 8x + 12

• 100 - 12 = 8x

• 88 = 8x

• x = 88/8

• x = 11 m

Now lets verify value of x

• 100 = 2 (x + 6 + 3x)

put value of x in this equation

• 100 = 2(11 + 6 + 3 ×11)

• 100 = 2(17 + 3 × 11)

• 100 = 2( 17 + 33)

• 100 = 2 (50)

• 100/(2×50) = 0

• 100/100 = 0

• 0 = 0

LHS = RHS

Hence verified !

Now Let's find dimensions:

• Breadth of rectangular garden = x
• Breadth of rectangular garden = 11 m

• Length of rectangular garden = 6 + 3x
• Length of rectangular garden = 6 + 3 × 11
• Length of rectangular garden = 6 + 33
• Length of rectangular garden = 39 m