Question

Express the following information in mathematical form using variables x and y.
i) The perimeter of a rectangle is 40 cm.
ii) The ratio of two numbers is 5:3
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Answer 1

The required mathematical expressions are

i) The perimeter of a rectangle 2(x + y) = 40

ii) The ratio of two numbers, x/y = 5/3

Given:

i) The perimeter of a rectangle is 40 cm.

ii) The ratio of two numbers is 5:3

To find:

Express the following information in mathematical form using variables x and y.

Solution:

Formula used:

Perimeter of rectangle = 2(Length + Width)

The ratio of two numbers a and b can be represented as follows

=> a: b = a/b

i) The perimeter of a rectangle is 40 cm.

Let x and y be the length and width of the rectangle

Using the formula,

Perimeter of rectangle = 2(x + y)

From the given data, Perimeter = 40

=> 2(x + y) = 40

ii) The ratio of two numbers is 5:3

Let x and y be the numbers

From the data, x : y = 5: 3

=> x/y = 5/3

Therefore,

The required mathematical expressions are

i) The perimeter of a rectangle 2(x + y) = 40

ii) The ratio of two numbers, x/y = 5/3

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Answer 2

Answer:

i. x + y = 20

ii. x = 5y/3

Step-by-step explanation:

i) Let the length and width of the rectangle be denoted by x and y, respectively. The perimeter of a rectangle is given by the formula P = 2(x + y). So, we can write:

2(x + y) = 40

Simplifying this equation, we get:

x + y = 20

Therefore, the sum of the length and width of the rectangle is 20 cm.

ii) Let the two numbers be denoted by x and y, and their ratio be 5:3. This means that:

x/y = 5/3

We can also express this as:

x = 5y/3

This tells us that the value of x is 5/3 times the value of y. We can use this relationship to solve various problems involving these two numbers, such as finding their sum or difference, or solving equations involving them.

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