Question

Prove that the area of an isosceles right triangle is one-fourth the square of the length of the hypotenuse.

Answer 1

Two sides equal in length

Answer 2

If I make a straight line dividing the isosceles triangle it makes two right triangles inside it

Answer 3

In order to prove this you need to set up an isosceles right triangle, find the area, find the length hypotenuse.

Answer 4

Thank you

Answer 5

how when there are no numbers provided?

Answer 6

You put in your own numbers, dummy numbers, or you can use letters to represent all numbers.

Answer 7

ok... thank you.

Answer 8

IF I plug in 5 for my base and 3 for my height I get an area of 7.5 I can calculate the hypotenuse 3^2 + 5^2 = c^2
9 + 25 = c^2
34 = c^2
5.83 as my third side...

Answer 9

what is my next step of how to prove the area of an isosceles triangle is one-fourth the square of the length of the hypotenuse?

Answer 10

is this it?

Answer 11

yes thank you

Answer 12

An isosceles right triangle is a 45-45-90 triangle with sides of x and hypotenuse of sqrt(2)x
x^2 +x^2 = (sqrt(2)x)^2
2x^2 = 2x^2
We know the area of triangle is 1/2 base*height, where base and height are both x
A = 1/2*x^2
Hypotenuse is sqrt(2)x -> Hypotenuse^2 = (sqrt(2)x)^2 = 2x^2
1/4*2x^2 = 1/2*x^2
Therefore Area is 1/4 of Hypotenuse^2

Answer 13

oh my goodness... you did good... I just have to understand it in english now lol thank you!!

Answer 14

your welcome
sorry i only speak english so cant help you there :)

Answer 15

lol