The area of a right angle is 49 sq. M. If one side is right and one side that makes a right angle is 14 units, how long is the other side that makes a right angle? Will be
Answers
Step-by-step explanation:
Given: Isosceles Triangle (ie - 2 sides equal)
Sides are: 3 cm and 7 cm
Find: 3rd side
Plan: Use the Triangle Inequality Theorem
There are 2 choices for the 3rd side of the triangle.
Choice 1: the 3rd side is 3 cm.
The Triangle Inequality states that the sum of any pair of a triangle’s sides is greater then the 3rd side.
Sides are: 3 cm, 3 cm, 7 cm In pairs:
Sum (7, 3) = 10 > 3 ok
Sum (7, 3) = 10 > 3 ok ( It’s an isosceles triangle so this happens twice.)
Sum (3, 3) = 6 not > 7 Fails
The sides cannot be 3 cm, 3 cm, 7 cm
Choice 2: the 3rd side is 7 cm
Sides are: 3 cm, 7 cm, 7 cm In pairs:
Sum (3, 7) = 10 > 7 ok
Sum (3, 7) = 10 > 7 ok ( occurs twice because it’s an isosceles triangle)
Sum (7, 7) = 14 > 3 ok
The Triangle Inequality Theorem is satisfied.
Thus, the 3rd side of the Isosceles Triangle is 7 cm. Q.E.D.
Double Check: ✅ ✅
Answer: 3rd side = 7 cm
Note:
“Q.E.D. or QED is an initialism of the Latin phrase "quod erat demonstrandum", literally meaning "what was to be shown".
First things first, let's explain what a right triangle is. The definition is very simple and might even seem obvious for those who already know it: a right-angled triangle is a triangle where one and only one of the angles is exactly 90°. The other two angles will clearly be smaller than the right angle because the sum of all angles in a triangle is always 180°.
In a right angled triangle the sides are defined in a special way. The side opposing the right angle is always the biggest in the triangle and receives the name of "hypotenuse". The other two sides are called catheti. The relationship between the hypotenuse and each of the cathetus is a very simple one, as we will see when we will talk about Pythagoras' theorem.