Question

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

Answer 1

Step-by-step explanation:

if h cm is the altitude,and x cm is it's corresponding base then h=5x/3

if height is (h+4),and base is (x-2)

then area 1/2.(h+4).(x-2)

so,1/2.x.h=1/2.(h+4).(x-2)

x.h=(h+4).(x-2)

x.5x/3=(5x/3 +4)(x-2)

5x^2/3=(5x+12)(x-2)/3

5x^2=5x^2+12x-10x-24

2x-24=0

x=24/2=12

h=12×5/3=20

so base is 12 cm and height is 20cm