Question

An altidude ofa triangle is five third the length of its corresponding base if altitude be increased by 4 cm and the base decreased by 2 cm the area of the triangle remains the same find base and the altitudes of the triangle

Answer 1

Answer:

12 cm and 20 cm.

Step-by-step explanation:

Let the base be '3a' and hence height should be 5/3 of 3a = (5/3 * 3a ) = 5a

Original height = 5a

Original base = 3a

When altitude is increased by 4 cm

and the base is decreased by 2 cm

New height = 5a + 4

New base = 3a - 2

Area of triangle = 1/2 * height * base

Here, area remains same:

= > 1/2 * 5a * 3a = 1/2 * (5a + 3)(3a - 2)

= > 5a*3a = (5a + 4)(3a - 2)

= > 15a² = 15a² - 10a + 12a - 8

= > 15a² - 15a² + 8 = 12a - 10a

= > 8 = 2a

= > 4 = a

Hence,

Original:

Height = 5a = 5(4) = 20

Base = 3a = 3(4) = 12