This question was uploaded on 07/09/21 on social media accounts.
In an isosceles triangle, one perpendicular is drawn from vertices (opposite to uncommon side) to its opposite side. From one of the vertices, two lines are drawn such that they will divide opposite sides (similar side) in the ratio 2:1:2. Find the fraction of area formed by two lines, vertices (from which two lines are drawn), and perpendicular lines.
Solution:
Explanation:
The explanation for 5a and 2a:
In two triangles (top of the areas marked by (1) and (2)) two angles are the same (on top vertices).
By this, they will divide bases in the ratio same as sides divide in the ratio (i.e. 5:2).
By keeping 'a' as constant, we get sides as 5a and 2a.
The explanation for 5b and 3b:
By applying the similar technique in triangles (same as above but this time (1) and (2) are included in respective triangles).
By keeping 'a' as constant, we get sides as 5b and 3b.
Explanation for (1) + (2) = s/5
Let us consider 2, 1, 2 as bases of the triangle with a common vertice.
These triangles will have the area in the ratio 2:1:2.
Triangle with base '1' will have 1/5 th of the total area of the triangle.
Puzzle based on Geometry, Area, Ratio, Triangle.
