Question

given that xy=3cm ,xzy 30 and yz=x , is it possible to solve x using the theorem of pythagoras ?
motivate your answer

Answer 1

Step-by-step explanation:

lets take AB=x

BC=3

AC=30

By theorem of pythagoras

AC2= AB2 +BC2

(30)2 = (x)2 + (3)2

900 = x2 + 9

-x2 = -900 + 9

-x2 = -891

x = root -891

x = 29.84

Answer 2

Right angled triangle :

  • A right angled triangle is the triangle with an angle 90°, i.e., a right angle.

  • By Pythagorean theorem, a right angled triangle will have a base (a), a height (b) and a hypotenuse (c) with the relation

a² + b² = c²

Solving the problem :

Given, XY = 3 cm, XZ = 30 cm and YZ = x cm.

• It is possible to find the value of x when XY, YZ, ZX form a right-angled triangle.
• We take XY² + YZ² = XZ² to find x.

Now, XY² + YZ² = XZ²

i.e., 3² + x² = 30²

or, 9 + x² = 900

or, x² = 891

or, x = 29.85 ( approximately )

Therefore, YZ = 29.85 cm.

Questions solved using Pythagoras theorem :

Question 1. The area of a right angled triangle whose base is 12.5 cm and height is 20 cm.

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Question 2. Arnob may want to borrow his cousin’s tent, which is shown below. He needs to determine x, the center height of the tent, to determine if it will be large enough for his camping trip. What is the center height of this tent, to the nearest tenth of a foot? 4.1 feet 8.1 feet 9.8 feet 12.0 feet

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