
Geometry
 Triangle Problems and Solutions 


Triangle, solved problems, examples 





Example:
Lengths of sides of a triangle are, a =
8 cm and b =
6 cm. How much is altitude
h_{b}
to the side b greater than the
altitude h_{a}
to the side a
if the length of the altitude h_{a} =
4 cm? 
Solution: Given,
a = 8 cm,
b = 6
cm and h_{a} =
4 cm.
h_{b}

h_{a} =
? 

Example:
The point of contact of incircle with radius 4
cm divides the side of a triangle to segments whose
lengths are, 6
cm and 8
cm. The length of the biggest side of the triangle is? 
Solution: Given,
r = 4 cm
and a
= 14 cm.
x
=
? 


Example:
A side of a triangle 

its angles,
b
= 30°
and g
= 45°, find the area of the 

triangle. 
Solution: Given,
side a,
b =
30° and g =
45°.
A_{D}
=
? 


Example:
The base of an isosceles triangle is 2
cm longer, and its equal sides
1
cm longer then the
altitude to the base. The
area of the triangle is? 
Solution: Given,
a =
h_{a} + 2
and b =
h_{a} + 1.
A_{D}
=
? 

Example:
A circle with the center at the center of an equilateral triangle intersects all three sides of the
triangle to three equal
parts each. Find the area of the parts of the triangle outside the circle if the side of the triangle
a =
Ö6. 
Solution: Given,
a =
Ö6.
A
=
? 

Example:
Lengths of sides of a right triangle are terms of an arithmetic
progression with the difference 2, find the radius of
incircle. 
Solution: Given,
a = x,
b = x + 2
and c =
x + 4.
r = ? 

Example:
A line parallel to the side AB, of a triangle
ABC, divides the triangle to two parts of the same
areas and intersects
the side AC at the point
A_{1} and the side
BC at the point
B_{1}. If radii of incircles of
triangles, ABC and
A_{1}B_{1}C are at
the same time legs of a right triangle whose hypotenuse length is
4Ö3, find the radius of the incircle of the
triangle ABC. 
Solution: 












Geometry
and use of trigonometry contents  A 



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