Question

A triangle is divided into 4 parts and the area of the 4 regions are given inside the corresponding regions. Find the value of x if the area of the triangle is 30.

Answer 1

Hint: In geometry, the area can be defined as the space occupied by a flat or the surface of an object.
Area is a measure of how much space there is on a flat surface. For example, two sheets of paper have twice the area of a single sheet, because there is twice as much space to write on.

Different shapes have different ways to find the area. For example, in a rectangle we find the area by multiplying the length times the width. In the rectangle above, the area is 2×4 or 8. If you count the small squares you will find there are 8 of them.
So the area of the large object is the sum of the area of the smaller objects that can be fitted inside the object. …(1)

Complete step-by-step answer:
Given the area of the triangle is 30
Using the concept (1) of hint:-
Area of the bigger triangle = area of part 1 + area of part 2+ area of part 3+ area of part 4
Where part 1, part 2, part 3 and part 4 are four areas enclosed completely inside the triangle and no space left.
$ \Rightarrow area = area1 + area2 + area3 + area4$
area 1= 8
area 2= 10
area 3= 5
area 4= x
By replacing the value of area 1, area 2, area 3 and area 4 we get the below equation
\[\Rightarrow 30 = 8 + 10 + 5 + x \]
Taking variable on one side and the constants on the other side
 \[\Rightarrow x = 30 - 8 - 10 - 5 \\
   \Rightarrow x = 30 - 23 \\
   \Rightarrow x = 7 \\
 \]
So, the area of the 4th part is 7.

Note: We often find the area of the room floor to determine the size of the carpet to be bought. Covering the floor with tiles, covering the wall with paint or wallpaper or building a swimming pool are other examples, where in the area is computed. We can use linear equations to solve these types of problems. We assume the unknown value to be any variable and then we equate the variable to other known values.