Given a triangle with perimeter 63 cm, one side of which is 21 cm, and one of the medians is perpendicular to one of its angle bisectors. Find the lengths of all sides of the triangle.

The lengths of all the sides of a triangle will be 21 cm

Explanation:

As we know the perimeter of a triangle = sum of all the sides. Let the three sides of the triangle be a, b, c . When the perpendicular bisect an angle the sides of the triangle become equal. As in the question one side is given 21 the other side also become 21. The perimeter is given 63.

According to the question,

AB=AC=21

AB+AC+BC= 63

21+21+BC=63

42+BC=63

BC=21

is this the complete

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3