An isosceles triangle is twice as tall as it is wide. Find the measurement of the congruent base angles
Answers
Answer:
The perimeter of an isosceles triangle can be calculated as:
P
=
2
a
+
b
, where
a
is the length of each of its legs and
b
is the base length.
If the perimeter of the triangle in our quesiton is is 50 cm, then:
50
=
2
a
+
b
b
=
50
−
2
a
.......................................................................................................................................(i)
Using the Pythagorean theorem, we can calculate the length of the altitude of the triangle as:
h
2
=
a
2
−
(
b
2
)
2
If the altitude is 5 cm, then:
25
=
a
2
−
(
b
2
)
2
25
=
a
2
−
b
2
4
100
=
4
a
2
−
b
2
...................................................................................................................(ii)
Substituting for equation (i) into equation (ii):
100
=
4
a
2
−
(
50
−
2
a
)
2
100
=
4
a
2
−
(
2500
−
200
a
+
4
a
2
)
100
=
4
a
2
−
2500
+
200
a
−
4
a
2
100
=
−
2500
+
200
a
200
a
=
2
,
600
Solving for a:
a
=
2600
200
=
13
c
m
Therefore, the length of the base is equal to:
b
=
50
−
2
a
b
=
50
−
2
(
13
)
b
=
24
c
m
Step-by-step explanation: