Question

the length of a rectangular field is 3 root 5 + 3 root 2 find the measure of its breadth such that the area of rectangle is a rational number

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Answer 1

The measure of its breadth can be $3 \sqrt{5}-3\sqrt{2}$.

Step-by-step explanation:

Consider the provided information.

It is given that the length of the rectangular field is $3 \sqrt{5} + 3\sqrt{2}$

As we know that the area of rectangle is $A=L\times B$

We need to find the measure of its breadth, so that area of rectangle is a rational number.

In order to make area rational number we will take B = $3 \sqrt{5}-3\sqrt{2}$ that will make the product a rational number.

$A=(3 \sqrt{5} + 3\sqrt{2})(3 \sqrt{5}-3\sqrt{2})$

Use the formula: $(a+b)(a-b)=a^2-b^2$

$A=(3 \sqrt{5})^2-(3 \sqrt{2})^2$

$A=(9\times 5)-(9\times2)\\A=45-18=27$

27 is a rational number.

Hence, the measure of its breadth can be $3 \sqrt{5}-3\sqrt{2}$.

#Learn more

How to solve irrational numbers​

https://brainly.in/question/9305495

Answer 2

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