Question

Please show steps :)

The area of a right triangle is 25.5 cm². What if it’s ankles measures 45°. What is the length of its hypotenuse?
A) 9.9cm
B) 7 cm
C) 8.9 cm
Or D) 10 cm

Answer 1

Anwser is d If not d than b

Answer 2

D

Explanation:

A triangle with the angles of 45, 45, and 90 will have equivalent side lengths and a hypotenuse longer than them by a factor of
`√(2)`. If the area of the triangle is 25.5 square centimeters, then you can find the lengths of the sides of the triangle. Since the area of a triangle is the base multiplied by the height and then divided by 2, the side lengths of the triangle must be
`√(25.5\cdot 2)=√(51)`. This means that the hypotenuse of the triangle must be
`√(51)\cdot √(2)=√(102)`, or a little over 10cm. Therefore, the answer I would pick is choice D. Hope this helps!