Question

an altitude of a triangle is five-thirds the length of its corresponding base if the altitude increased by 4 cm and the base be decreased by 2 centimetre the area of the triangle would remain the same find the base and the altitude of the triangle

Answer 1

Answer:

Step-by-step explanation:

h=5/3b

3h=5b

Area=1/2*b*h=1/2*b*(5/3)b=1/2*(5/3)*b^2

base is decreased by 2 and height is increased by 4

Area=1/2*(b-2)*(h+4)

Area is same

1/2*(b-2)*(h+4)=1/2*(5/3)*b^2

(b-2)*(5b/3+4)=5/3b^2

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

5b^2+12b-10b-24/3=5/3(b^2)

5b^2+2b-24=5b^2

b=12

h=5/3b

h=20