Answer: The distance from vertex B to vertex H is 6.9 inches.
Step-by-step explanation:
The length of the line BH can be thought of as the hypotenuse of a triangle rectangle where the catheti are the lines HD (whit a measure of 4in) and line DB.
The length of the line DB can be thought of as the hypotenuse of a triangle rectangle where the catheti are lines DA and AB (both are 4in long)
Then if we use the Pythagorean's theorem, the length of line DB is:
(DB)^2 = (DA)^2 + (AB)^2
(DB)^2 = (4in)^2 + (4in)^2 = 32in^2
(DB) = √(32in^2) = 5.66 in
Whit this, we can find the length of line HB as:
(HB)^2 = (HD)^2 + (DB)^2
(HB)^2 = (4in)^2 + (DB)^2 = 16in^2 + 32in^2 = 48in^2
HB = √(48in^2) = 6.93 in
If we round to the nearest thent, we get:
HB = 6.9 in
The distance from vertex B to vertex H is 6.9 inches.
