an altitude of a triangle is 5 by 3 times the length of its corresponding base if the altitude is increased by 4 cm and the base is decreased by to the area of the triangle remains the same find the altitude and the base of the original triangle
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Answer:
Let the length of corresponding base be x.
Thus, altitude will be 35x.
Now, it is given that altitude is increased by 4 cm i.e., 35x+4 and base is decreased by 2 cm i.e., x−2.
The area is same for both.
Therefore, 21×x×35x=21×(35x+4)×(x−2)
⇒35x2=35x2−310x+4x−8
⇒8=32x
⇒x=12
Thus, length of base is 12 cm
and length of altitude is 35×12=20 cm.
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