Question

13. The base of a triangle is 3/4th on the length of the corresponding altitude. if the altitude is increased by 3 cm
and the base is decreased by 2 cm, the area of the triangle remains the same. Find the base and attitude of the triangle.
of the triangle
same distance upstream in​

Answer 1

Answer:

24 cm and 18 cm

Step-by-step explanation:

Let the height be '4a' and hence base should be 3/4 of 4a = (3/4 * 4a ) = 3a

Original height = 4a

Original base = 3a

When altitude is increased by 3 cm

and the base is decreased by 2 cm

New height = 4a + 3

New base = 3a - 2

Area of triangle = 1/2 * height * base

Here, area remains same:

= > 1/2 * 4a * 3a = 1/2 * (4a + 3)(3a - 2)

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

= > 12a² = 12a² - 8a + 9a - 6

= > 12a² - 12a² + 6 = 9a - 8a

= > 6 = a

Hence,

Original:

Height = 4a = 4(6) = 24

Base = 3a = 3(6) = 18