Question

Why is the answer D? Plz explain.

Answer 1

BD is the hypotenuse of right triangle BED.
In right triangle BED, the legs are BE and ED.
BE = BA + AE

AB = 3; BC = 5

Use the Pythagorean theorem to find AC.

3^2 + (AC)^2 = 5^2

(AC)^2 = 25 - 9

AC = 4

ACDE is a square, so AE = AC = ED = 4

BE = BA + AE 3 + 4 = 7

Use the Pythagorean theorem to find the length of the hypotenuse, BD.


`a^2 + b^2 = c^2`


`(BE)^2 + (ED)^2 = (BD)^2`


`7^2 + 4^2 = (BD)^2`


`49 + 16 = (BD)^2`


`(BD)^2 = 65`


`BD = √(65)`

Answer 2

ΔABC is a right triangle
By the Pythagorean theorem:
AC = √(BC² - AB²) =√(5²-3²) = √(25-9) = √16 = 4

ΔBED is a right triangle
DE = 4
BE = AB + AE = 3 + 4 = 7
By the Pythagorean theorem:
BD = √(BE² + DE²) =√(7²+4²) = √(49+16) = √65

Answer: BD = √65