Question

the altitude of a triangle is three fifth of the length of the corresponding base if the altitude is decreased by 4 cm and the corresponding base is increased by 10 cm the area of a triangle remains same find the base and altitude of the triangle​

Answer 1

Dear Student,

◆ Answer -

b = 20 cm

h = 12 cm

● Explaination -

Let b be base and h be altitude of the initial triangle.

h = 3b/5

Let b' be base and h' be altitude of the final triangle. Area of initial and final triangle is same.

b.h = b'.h'

b.h = (b+10)(h-4)

b.h = (b+10)(h-4)

b×3b/5 = (b+10)(3b/5-4)

3b²/5 = 3b²/5 + 30b/5 - 4b - 40

3b²/5 - 3b²/5 + 6b - 4b = 40

2b = 40

b = 20 cm

Now, altitute is -

h = 3b/5

h = 3 × 20/5

h = 12 cm

Therefore, height of triangle is 12 cm and base is 12 cm.

Hope thats all...