an altitude of a triangle is 5 by third the length of its corresponding base if the altitude is increased by 4 cm and the base is decreased by 2 cm the area of a triangle would remain the same find the base and 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:
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