Question

In an isosceles triangle ABC, if AB = AC=13 cm and the altitude from A on BC is 5 cm find BC.

Answer 1

since this is an isosceles triangle we could split and have a perpendicular bisector. since it is a bisector we know the bottom part of it would be 5 (half of 10) and the hypotenuse would be 13. this is a right triangle since the line we got was a perpendicular bisector.

using the Pythagorean theorem we get height perpendicular bisector is 12.
${13}^2-5^2=144={12}^2$ so the side is 12 and it would be the altitude to BC

now we find the area which is $\frac{1}{2}\times b\times h$ we got the height which is 12 when the base is 10

so area will be

$\frac{1}{2}\times 12\times 10=60$

using AB as the base the perpendicular which is the height would be solved by

2 A / b = h

120 / 13 would be the altitude to BC