# How To Do These Pythagorean Theorem Math Questions?

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Hi all, here are some questions for the past day I am not able to absolutely understand could someone please give me explanations on how to solve these? I will put the pictures below.

This is #9 the question

This is #9c I am unable to solve this

This is number #3 and # 5 I am unable to solve this

I understand all of you are very busy! If you are able to answer all of these hopefully simple questions, I'd really appreciate it!

Hi all, here are some questions for the past day I am not able to absolutely understand could someone please give me explanations on how to solve these? I will put the pictures below.

This is #9 the question

This is #9c I am unable to solve this

This is number

I understand all of you are very busy! If you are able to answer all of these hopefully simple questions, I'd really appreciate it!

##### 3 Answers

Answer to ex. 9c:

Answer to ex. 3: the perimeter is

Answer to ex. 5: the side of the square is

#### Explanation:

**Answer to ex. 9c:**

Let C be the intersection of MN with AB:

the triangles AMC and NBC are similar

(

let

that's

Then AB=AC+BC and, by the Pythagoras theorem, it is:

**Answer to ex.3**

Let x the lower side of the rectangle, then the greater one will be 2x, then let's solve the equation:

Then the perimeter is:

and the area is:

**Answer to ex. 5**

In a square the relation between side and diagonal is:

diagonal=side

Then side=diagonal

#### Explanation:

Please see the diagram below for reference.

Here we have extended

Now as

Similarly

Now as

and

(3) Perimeter

Area

(4)Side of square

(9)

#### Explanation:

(3) Let

Length of other side is

Therefore,

Perimeter

Area

(5)Let

(9c) Easier way to calculate

Let

Let

Triangles OMA and ONB are similar

Therefore,

Finally,

I hope that this will help!!!