An altitude of a triangle is five thirds the length of its corresponding base. If the altitude were to be increased by 4cm and the base be
decreased by 2cm, the area of the triangle could remain the same. Find the base and the altitude of the triangle.
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Answer:
Let the length of corresponding base be x.
Thus, altitude will be
3
5
x.
Now, it is given that altitude is increased by 4 cm i.e.,
3
5
x+4 and base is decreased by 2 cm i.e., x−2.
The area is same for both.
Therefore,
2
1
×x×
3
5
x=
2
1
×(
3
5
x+4)×(x−2)
⇒
3
5
x
2
=
3
5
x
2
−
3
10
x+4x−8
⇒8=
3
2
x
⇒x=12
Thus, length of base is 12 cm
and length of altitude is
3
5
×12=20 cm.
Step-by-step explanation: