in an isosceles triangle the vertex angle measures 90 degrees and the length of each congruent leg is 5√2. whats the length of the base?

Isn't the base the hypotenuse of a right-angled triangle?

so h^2 = (5√2)^ + (5√2)^2
= .......

How did you come up with that?

i put it into the calculator and i got 20

oohh okay i get it now

thank you soo muchh!

To find the length of the base in an isosceles triangle, we can use the Pythagorean theorem. In an isosceles triangle with a vertex angle measuring 90 degrees, the two congruent legs are the same length.

Let's assume that the length of each congruent leg is "x." In this case, x = 5√2.

Using the Pythagorean theorem, we can write the equation:
(base)^2 + (leg)^2 = (hypotenuse)^2

Since we know the vertex angle is 90 degrees, the hypotenuse is equal to the length of the congruent leg, which is x.

Plugging in the values, we get:
(base)^2 + (5√2)^2 = (5√2)^2

Simplifying:
(base)^2 + 25(2) = 25(2)

Further simplification:
(base)^2 + 50 = 50

Next, we can isolate the base term by subtracting 50 from both sides:
(base)^2 = 0

To solve for the base, we can take the square root of both sides:
base = √0

Since the base is equal to the square root of zero, the length of the base in this isosceles triangle is 0. This indicates that the triangle is degenerate, with overlapping legs forming a straight line.

20?

You should not need a calculator.

h^2 = (5√2)^ + (5√2)^2
= 50 + 50
= 100
h = √100 = 10