Q19 of 46 Page 175

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.

Let, base of the triangle = x cm


∴ altitude of the triangle = 5x/3 cm


∴ area of the triangle = 1/2 × x × 5x/3 = 5x2/6


In 2nd case,


Base of the triangle = x – 2 cm


Altitude of the triangle = (5x/3) + 4


∴ area of the triangle = 1/2 × (x – 2) × (5x/3 + 4)


= 5x2/6 + 2x – 5x/3 – 4


According to problem,


⇒ 5x2/6 = 5x2/6 + 2x – 5x/3 – 4


⇒ x/3 = 4


⇒ x = 12


∴ Base = 12 cm


∴ Altitude = 5 × 12/3 = 20 cm

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