FIND THE MISSING SIDE LENGTH USING PYTHAGOREAN THEOREM

For each triangle find the missing length. Round your answer to the nearest tenth. Then find the area and the perimeter.

Problem 1 :

Solution :

Let the missing side be x.

hypotenuse = 19

x² + 17² = 19²

x² + 289 = 361

x² = 361 - 289

x² = 72

x = √72

x = 8.48

Problem 2 :

Solution :

Let the missing side be x.

hypotenuse = x

5² + 13² = x²

25 + 169 = x²

x² = 194

x = √194

x = 13.92

Problem 3 :

Find a third number so that the three numbers form a right triangle:

i) 9 , 41

Solution :

Let x be the unknown.

In the given measure 41 is the greatest.

41² = 9² + x²

1681 = 81 + x²

Subtracting 81 on both sides.

1681 - 81 = x²

x² = 1600

x = √1600

x = 40

Problem 4 :

Ms. Green tells you that a right triangle has a hypotenuse of 13 and a leg of 5. She asks you to find the other leg of the triangle. What is your answer?

Solution :

Hypotenuse = 13, one leg = 5, other leg = x ?

x² + 5² = 13²

x² + 25 = 169

x² = 169 - 25

x² = 144

x = √144

x = 12

Problem 5 :

The sides of a triangle have lengths x, x + 5, and 25. 

If the length of the longest side is 25, what value of x makes the triangle a right triangle?

Solution :

Longest side = 25

25² = x² + (x + 5)²

625 = x² + x² + 2x(5) + 5²

625 = 2x² + 10x + 25

2x² + 10x + 25 - 625 = 0

2x² + 10x - 600 = 0

Dividing by 2, we get

x² + 5x - 300 = 0

(x - 15)(x + 20) = 0

x = 15 and x = -20

Since x is one of the side of the triangle, we ignore -20.

So, the value of x is 15.

Problem 6 :

A 22 foot ladder lean against a shed reaching a height of x feet. The base of the ladder is 10 feet from the shed.

Solution :

22² = x² + 10²

484 = x² + 100

x² = 484 - 100

x² = 384

x = √384

x = 19.59

Approximately height of the wall is 19.6 feet.