Question

Calcula los lados desconocidos del siguiente triángulo sabiendo que el perímetro mide 36 cm, el lado BC 10 cm y la altura sobre el lado mayor, AB, mide 8 cm

Answer 1

AC = 11.6 cm

AB = 14.4 cm

Explanation:

To make the solution easier, we can draw the triangle, as in the image attached.

Let's call the side AC = x, and the bigger side AB = y

The height of 8 cm divide the bigger side in two parts, a and b, in the point H.

In the triangle CHB, we can use pythagoras formula to find the value of a:

a^2 + 8^2 = 10^2

a^2 = 100-64 = 36

a = 6

then, we have that a + b = y -> b = y - 6

Now, using the pythagoras formula in triangle CHA:

8^2 + (y-6)^2 = x^2

64 + y^2 - 12*y + 36 = x^2

x^2 - y^2 + 12*y = 100

From the perimeter of the triangle, we have that:

x + y + 10 = 36 -> x + y = 26 -> x = 26 - y

Then, using this value of x in the equation above, we have:

(26 - y)^2 - y^2 + 12*y = 100

676 - 52*y + y^2 - y^2 + 12*y = 100

40*y = 576

y = 14.4 cm

Now we can find x:

x = 26 - y = 26 - 14.4 = 11.6 cm