The legs of an isosceles triangle are 13 units long and the altitude to the base is 12 units long.?

Question

find the length of the base.

Answer 1

The base is 10 units.

The isosceles triangle can be seen as two back-to-back right triangles... with a height of 12 units and the hypotenuse is 13 units.

Using pythagorean theorem, a^2 + b^2 = c^2
where a is unknown base length, b is the height (12 units) and c is the hypotenuse (13 units)... solving for a

a = sqrt(13^2 - 12^2)
a = 5 units

as mentioned above the isoceles is like two back-to-back right triangles so the isosceles base = 2a = 2 x 5 = 10 units.

Answer 2

Ther construction line for the height makes 2 right triangles with sides of 12, 13, and an unknown (x), which is 1/2 the base of the isoceles triangle.

Use Pythagorean:

12^2 + X^2 = 13^2

Solve for X, multiply by 2 to get length of base.

Answer 3

This forms a triangle with two equal sides

Therefore you have two equal triangles with a common base
and a common altitude and hypotenuse.

Let 1/2 x = length of base of one triangle

The formula to find the length of this base is:

the root of (hypotenuse squared) - ( altitude squared)

This equals: the root of ( 13 squared - 12 squared)

Root of ( 169 - 144 ) = root of 25 = 5

Therefore the base of one triangle is 5 and the other is also 5
therefore the length of the base of the isosceles triangle is 10

Answer 4

10

Answer 5

Isosceles triangle, ABC, AB = AC = 13
Draw altitude AD meeting BC at D
AD = 12
BD = CD

Pythagorus theorem
BD^2 = AB^2 - AD^2 = 13^2 - 12^2 = 25
BD = 5

BC = 2 BD = 2 * 5 = 10

Length of base = 10

Answer 6

Turn it into two right triangles, then use the Pythagorean Theorem. If you do it right, you'll get 10 as the answer.

Answer 7

use pythagorean theorum.
*s.=squared*

13sq. = 12sq. + bsq./2
169=288/2+bsq./2
2x169=288+bsq.
338=288 + bsq.
50=bsq.
b=7.07 units.