Question

The altitude of a triangle is two-third the length of its corresponding base. If the altitude increased by 4cm and the base decreased by 2cm, the area of the triangle remains the same. Find the base and the altitude of the triangle.

Answer 1

ANSWER:-

Given:

The altitude of a triangle is two-third the length of its corresponding base. If the altitude increased by 4cm and base decreased by 2cm, the area of triangle remains the same.

To find:

Find the base and Altitude of the triangle.

Solution:

Let the length of the altitude & base of a triangle be L cm and B cm

According to the question;

$L= \frac{2}{3} B..........(1)$

We know that area of triangle is;

=) 1/2 ×(base × height)

$= > \frac{1}{2} (L + 4)(B - 2) = \frac{1}{2} L\times B$

Putting equation (1), we get;

$= > ( \frac{2}{3} B + 4)(B - 2) = \frac{2}{3} B \times B \\ \\ = > \frac{2}{3} {b}^{2} + 4B - \frac{4}{3} B - 8 = \frac{2}{3} {B}^{2} \\ \\ = > \frac{12B - 4B}{3} = 8 \\ \\ = > \frac{8B}{3} = 8 \\ \\ = > 8B= 24 \\ \\ = > B= \frac{24}{8} \\ \\ = > B = 3$

Therefore,

L= 2/3B

=) L= 2/3× 3

=) L= 2cm

Hence,

The base of the triangle is 3cm & altitude of the triangle is 2cm.

Hope it helps ☺️