Question

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

Answer 1

To find the base and altitude of the triangle, set up an equation using the given information and solve for the variables.

Step-by-step explanation:

Let's assume the length of the base of the triangle is 'x'.

According to the given information, the altitude of the triangle is three-fifths of the length of the base. So, the altitude can be expressed as (3/5)x.

When the altitude is decreased by 4cm and the corresponding base is increased by 10cm, the area of the triangle remains the same.

Using the formula for the area of a triangle (A = 1/2 × base × height), we can set up the following equation:

1/2 × (x + 10) × [(3/5)x - 4] = 1/2 × x × ((3/5)x)

Solving this equation will give us the values for the base and altitude of the triangle.