The sum of lengths of legs of the right triangle is 15 cm. Find the area of a square inscribed in the triangle if the length of the hypotenuse is 3root13 cm.
Answers
Answer:
Step-by-step explanation:
Is there a simple relationship between the length of the sides of a triangle? Apart from the fact that the sum of any two sides is greater than the third, there is, in general, no simple relationship between the three sides of a triangle.
Among the set of all triangles, there is a special class, known as right-angled triangles or right triangles that contain a right angle. The longest side in a right-angled triangle is called the hypotenuse. The word is connected with a Greek word meaning to stretch because the ancient Egyptians discovered that if you take a piece of rope, mark off 3 units, then 4 units and then 5 units, this can be stretched to form a triangle that contains a right angle. This was very useful to the Egyptian builders.
This raises all sorts of questions. What is so special about the lengths 3, 4 and 5? Are there other sets of numbers with this property? Is there a simple relationship between the lengths of the sides in a right-angled triangle? Given the lengths of the sides of a triangle, can we tell whether or not the triangle is right angled?
Most adults remember the mathematical formula
c2 = a2 + b2
or perhaps
“the square on the hypotenuse is the sum of the squares on the other two sides.”
The first version uses an implied standard notation, the second version uses archaic language but both are Pythagoras’ theorem. This theorem enables us to answer the questions raised in the previous paragraph.
The discovery of Pythagoras’ theorem led the Greeks to prove the existen