Question

altitude of a triangle is five third times the base. if the altitude is increased by 4 and the base is decreased by 2 the area of the triangle would remain the same then altitude and the base are

Answer 1

Answer:

Altitude = 20 units

Base = 12 units

Step-by-step explanation:

Let original value of Altitude =  5x

and original value of base = 3x

The area of the triangle is $\frac{1}{2}$(3x)(5x) = $\frac{15x^{2} }{2}$

In the second case, the altitude is (5x + 4) and the base is (3x - 2)

The area will be  $\frac{1}{2}$(5x + 4)(3x - 2)

It is given that the areas are equal. On equating them, we get

 $\frac{1}{2}$(15x²) =   $\frac{1}{2}$(5x + 4)(3x - 2)

15x² = 15x² - 10x + 12x - 8

2x = 8

so x = 4.

The altitude is 5(4) = 20 units and the base is 3(4) = 12 units.