In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 5 in.? 25√ in. 52√ in. 5√ in. 55√ in.

Step-by-step explanation:

Given: In a 45-45-90 triangle, the length of one of the legs= 5 in.

Let H be the hypotenuse of the given right triangle.

Since the two angles are equal (45°) in the given right triangle,also in a triangle the side opposite to the equal angles are equal.

Therefore, the other leg of given right triangle = 5 in.

Now applying Pythagoras theorem, we get

Hence, the length of the hypotenuse =

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.