Question

The sides of a triangle are in the ratio 3:5:7 and its
perimeter is 75 cm, then the length of longest altitude is

Answer 1

Answer:

is this is a question of herons formula

sorry I don't have time so by easy method my answer is 5 cm

Answer 2

Given:

The sides of a triangle are in the ratio of 3:5:7

The perimeter of the triangle is 75cm.

To Find:

The length of the longest altitude of the triangle.

Solution:

Let the three sides of the triangle be 3x, 5x, 7x.

The perimeter of the triangle = Sum of the three sides

                                     75cm  = 3x + 5x + 7x

                                      75cm = 15x

                                             x = 75/15

                                             x = 5

So, the sides of a triangle = 15 + 25 + 35

Now, Area of the triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

                                          = $\frac{15 + 25 + 35}{2}$

                                          = $\frac{75}{2}$

                                          = $\sqrt{\frac{75}{2}*\frac{45}{2}*\frac{35}{2}*\frac{5}{2} }$

                                          = $\frac{375}{4}\sqrt{3}$

The length of the longest altitude = $\frac{2(area of triangle)}{smallest base}$

                                                         = $\frac{2*\frac{375}{4}\sqrt{3} }{15}$

                                                         = $\frac{375}{30}\sqrt{3}$

                                                         = $\frac{25}{2}\sqrt{3}$

Therefore, the length of the altitude = $\frac{25}{2}\sqrt{3}$.