Can someoneexplain . how long is the hypotenuse of an isosceles right triangle whose area is 4?

4 units long.

Step-by-step explanation:

The 2 legs of an isosceles right angles triangle are equal .

So the area = 1/2 * x^2     where x = length of a leg.

1/2x^2 = 4

x^2 = 8

x = √8

So the length of the hypotenuse is found using the Pythagoras theorem:-

h^2 =   (√8)^2 +  (√8)^2

h^2 = 16

h = 4  (answer).

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.