Math is an essential subject for almost every competitive examination including the SAT and ACT. Getting the fundamentals right is quite important when it comes to solving complex problems in Math. A lot of students find it difficult to memorize the steps and recollecting the Mathematical formulae during the test prep. With the additional pressure of competitive examinations, the student’s woes are doubled.  

Basic Terminologies relating to finding the base of a Triangle: 

What is a base?
Base means bottom. 

What is the height?
The height of any object is how much it measures from its top to its bottom. 

How do you identify the base of a triangle?
Any of the three sides of a triangle can be considered the base of the triangle. 

How do you identify the height of a triangle?
The height of a triangle is the perpendicular line dropped onto its base from the corner opposite the base. 

 As Turito understands this difficulty and in order to address the issue, we bring you the ways in which one can find the base of a Triangle. 

  1. Way to find the triangle base from the area of the triangle: 

            Area of the triangle= ½ bh  

            Where b- base 

             h- height 

Once the area of the triangle is found, the area formulae can be applied to A=1/2 bh in reverse approach to get the length of the base. So, the formula for the base of the triangle is 

             b=2A/h 

       2. Ways to find the triangle base from a right-angled triangle: 

One can apply the Pythagorean theorem, or use the formula which involves the length of two sides or the hypotenuse.  The reverse technique helps even in this regard. 

Source: https://tutorme.com/blog/post/how-to-find-the-base-of-a-triangle/ 

Even if the area value is not known,  but know the length of the triangle- this formula can be used. In the right-angled triangle, the height and the base have the same length.  

       3. Way to find triangle base of an Isosceles Triangle: 

 It is well-known fact that an isosceles triangle has two sides that have an equal length. 

a is the length of the two known sides of the isosceles that are equivalent. 

       4.Way to find the base for Equilateral Triangle: 

 An equilateral triangle has all the sides in equal length.   The regular area of the triangle formula applies here 

Visualize the equilateral triangle as two smaller right triangles in order to find the height, where the hypotenuse is the same length as the side length b. By the 30-60-90 rule, a special case of a right triangle, we know that the base of this smaller right triangle is  and the height of this smaller right triangle is , assuming b to be the hypotenuse. 

After finding the height, use it in the following formula by adding area and height values: 

 And substitute  for the height: 

Tools to use for finding the base of a triangle: 

The Pythagorean Theorem: This equation shows the relationship between a right triangle’s three sides, finding the area is easier. 

A triangle that contains a 90-degree or right angle in one of its three corners is called a right triangle. A right triangle’s base is one of the sides that adjoins the 90-degree angle. 

All about Pythagoras-  the creator of this resourceful formula: 

Pythagoras, who hails from Greece, is often linked with the discovery of the mathematical theorem still used today to calculate the dimensions of a right triangle. To complete the calculations, you must know the dimensions of the longest side of the geometric shape, the hypotenuse, as well as another one of its sides. 

The legendary Mathematician migrated to Italy in about 532 BCE because of the political and social conditions of the country. Pythagoras also determined the significance of numbers in music. Unfortunately, most of his works are not documented, which is why scholars don’t know if it was Pythagoras himself who discovered the theorem or one of the many students or disciples who were members of the Pythagorean brotherhood, a religious or mystical group whose principles influenced the work of Plato and Aristotle. 

Effective tips for finding the base of the triangle: 

  1. Know the types of the triangles first: It is important to know the classification for triangle- names Isosceles, Equivalent, Right-Angled, and Scalene Triangle.  

 Isosceles Triangle: Our of the three sides, two sides are in equal length for this type of triangle. 

 Equivalent Triangle: The three sides of this triangle are equal in length. 

 Right-Angled: In this triangle, one side is the longest compared to the other two sides and it is termed as the hypotenuse.  

 Scalene:  Here, all the sides of the triangle are unequal. Solving problems and finding the area and base of this triangle is tricky to find.  

  1. Memorize the formulae: The student is expected to memorize all the formulae associated with finding the area, length of the triangle. This will save time to find the solution in an effortless manner.
  2. Think out of the box: Though Math is a subject that depends on step by step sequence of solving a problem, at times- the idea of reverse engineering to get the answer. Especially when it comes to competitive examinations, time is a valuable resource. Hence, thinking out of the box will make finding solutions easier. 

The Final Word: 

Finding the base of the triangle depends on the type of the triangle with respect to the length, and the student is expected to memorize the formulae to use them accordingly to get the solution.  Taking the right guidance from the tutor, and enrolling in a course can easily help the student to build strong fundamentals.  

Math is a subject that is heavily concept-dependent and having strong and fundamentals will greatly help the student in the long run- whether in competitive exams or pursuing a career in the subject.