**Real World Problems on Pythagorean Theorem :**

Here we are going to see some practice problems on pythagorean theorem.

**Question 1 :**

A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?

Solution :

the distance of his current position from the starting point = √18^{2} + 24^{2}

= √(324 + 576)

= √900

= 30 m

Hence the required distance is 30 m.

**Question 2 :**

There are two paths that one can choose to go from Sarah’s house to James house. One way is to take C street, and the other way requires to take A street and then B street. How much shorter is the direct path along C street? (Using figure).

**Solution :**

By choosing the C street, he has to cover the distance,

= √2^{2} + 1.5^{2}

= √(4 + 2.25)

= √6.25

= 2.5 miles

By choosing the alternative way, he has to cover the distance = 2 + 1.5

= 3.5 miles

The difference between these two paths = 3.5 - 2.5

= 1 mile

Hence by choosing the direct path, he may save 1 miles faster than other way.

**Question 3 :**

To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?

**Solution :**

By drawing the rough picture using the given information, we get

AC = √34^{2} + 41^{2}

= √1156 + 1681

= √2837

= 53.26

Miles saved = (34 + 41) - 53.26

= 75 - 53.26

= 21.74 m

**Question 4 :**

In the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle?

**Solution :**

XY + YZ = 17 cm

XZ + YW = 26 cm

To calculate : - Length and breadth of the rectangle.

We know that,

Diagonals of a rectangle are equal.

So, XZ = YW

Then, XZ = YW = 26/2 = 13 cm

Now,

In ∆XYZ ,

Let YZ = P , Then, XY = (17 - P).

Then, by Pythagoras theorem,

(P)² + (17 - P)² = (13)²

P² + 289 - 34P + P² = 169

2P² - 34P = 169 - 289

2(P² - 17P) = - 120

P² - 17P = - 120/2

P² - 17P = - 60

P² - 17P + 60 = 0

P² - 12P - 5P + 60 = 0

P(P - 12) - 5(P - 12) = 0

(P - 12)(P - 5) = 0

P - 12 = 0, P = 12

P = 12 cm

Again,

P - 5 = 0 => P = 5 cm

Now,

YZ = P = 12 cm [Because , YZ is the length of the rectangle ,so we will assign it the greatest value of P]

Again, XY = (17 - P) = (17 - 12) cm = 5 cm

[Because , XY is thee breadth.]

After having gone through the stuff given above, we hope that the students would have understood, "Real World Problems on Pythagorean Theorem".

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