Question

What is the height of a triangle if the base is 10 cm and the sides are 13 cm

Answer 1

because the sides are the same it is an isosceles triangle, therefore the altitude forms two right triangles and also bisects the base

Apply the Pythagorean Theorem
5^2 + h^2= 13^2

25+h^2= 169
h^2= 144
h=12

FYI there are familiar combinations for right triangles, might be worthwhile to check them out, it will save a lot of time.

Some examples are 3,4,5 / 5,12. 13 / 9,40,41 etc

Hope this helps

Answer 2

if the sides (plural, meaning more than 1) and the base is 10

that means
2 sides=13 cm
base=10
since 2 sides equal legnths, isocolees
draw a line from the top angle, opposite the base side, perpendicular to the base
you will form 2 right triangles each with a base of 10/2=5 and a hypotonuse of 13 solve for other leg

a^2+b^2=c^2
c=hypotonuse=13
a=10=1 leg
b=mystery leg (height)

10^2+x^2=13^2
100+x^2=169
subtract 100 from both sides
x^2=69
take square root of both sides
x=√69

it would be safe to put √69 as the answe since it cannot be simplified into a whole number (about 8.3066238629181)