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 answer is not 21, 21, and 21

The lengths of all sides of the triangle will be 21 cm, 21 cm, and 21 cm

Step-by-step explanation:

Given that the perimeter of the triangle = 63 cm

And the length of one side = 21 cm

and one of the medians is perpendicular to one of its angle bisectors

Since triangle has 3 sides,

Median = 63 ÷ 3 = 21

Therefore each side length = 21 cm

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15