Question

The altitude of a triangle is five- thirds the length of its corresponding base. If the altitude is increased by 4 cm and the base decreased by 2 cm, the area of the triangle would remain the same. Find the base and altitude of the triangle.​

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The altitude of a triangle is five- thirds the length of its corresponding base. If the altitude is increased by 4 cm and the base decreased by 2 cm, the area of the triangle would remain the same. Find the base and altitude of the triangle

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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