Plz help, will give brainllest to the one correct
1 answer:
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Answer:
AC = 11.6 cm
AB = 14.4 cm
Step-by-step 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
