Question

The rectange below is
twice as long it is wide
What is the ratio of the
width of the rectangle to its perimeter ​

Answer 1

Given:

The rectangle below is twice as long it is wide

To find:

What is the ratio of the width of the rectangle to its perimeter?

Solution:

Let,

"l" → represents the length of the given rectangle

"w" → represents the width of the given rectangle

The rectangle is twice as long it is wide, therefore, we get

l = 2w . . . . Equation 1

We know,

$\boxed{\bold{Perimeter \:of\:a\:rectangle = 2 (length + width)}}$

By using the formula above, we get

The perimeter of the given rectangle is,

= 2 (l + w)

substituting from equation 1

= 2 (2w +w)

= 2 × 3w

= 6w

Now,

The ratio of the width and the perimeter of the rectangle is,

= $\frac{Width}{Perimeter}$

= $\frac{w}{6w}$

= $\bold{\frac{1}{6}}$

Thus, the ratio of the width of the rectangle to its perimeter is → 1 : 6.

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Answer 2

SOLUTION

GIVEN

The rectangle below is twice as long it is wide

TO DETERMINE

The ratio of the width of the rectangle to its perimeter

CONCEPT TO BE IMPLEMENTED

Ratio :

Ratio means comparing of two quantities

The ratio of a number a to another number b ( where b # 0) is a fraction a/b and it is written a : b , the first term a is called antecedent and the second term is called consequent

EVALUATION

Let width of the rectangle = x

Then length = 2x

So perimeter

= 2 × ( Length + Width )

= 2 × ( 2x + x )

= 2 × 3x

= 6x

So the required ratio of the width of the rectangle to its perimeter

= x : 6x

= 1 : 6

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