What is the height (one of the legs) and the hypotenuse of an isosceles right triangle that has an area of 800 square feet?

14

√

2

=

7

√

2

Step-by-step explanation:

An isosceles right triangle is a right triangle with two legs equal in length and has angles of

45

∘

−

45

∘

−

90

∘

.

By Pythagorean Theorem, we know that,

hypotenuse

c

2

=

a

2

+

a

2

,

⇒

c

=

a

√

2

where

c

is the hypotenuse and

a

is the leg.

So for an isosceles right triangle with side length

a

, the hypotenuse has a length of

a

√

2

.

Similarly, if the hypotenuse of an isosceles right triangle has length of

a

, the legs have a length of

a

√

2

or

a

√

2

2

each.

Given that the hypotenuse of the isosceles right triangle

=

14

,

⇒

the length of each leg

=

14

√

2

=

7

√

2

Check :

(

7

√

2

)

2

+

(

7

√

2

)

2

=

196

=

14

2

(OK)

1e+27

step-by-step explanation: