Answer:
d.
Explanation:
this is written to NOT confuse you by having too many things in one answer option.
we need to find x and y, and thereby identify the correct answer option out of the 4 given options.
we know Pythagoras for right-angled triangles :
a² + b² = c²
c is the Hypotenuse (the side opposite of the 90°angle).
a, b are the legs.
x² + 5² = y²
I am not sure if you know the trigonometric functions already.
so, skipping this we solve by trying the answer options in the Pythagoras formula above, and see, for which answer the equation is true :
(10sqrt(3)/3)² + 25 = (5sqrt(3)/3)²
100×3/9 + 25 = 25×3/9
100/3 + 25 = 25/3
a. is definitely wrong, as 25 by itself is already much larger than 25/3, and then we are adding 100/3. no equality.
(5sqrt(2)/2)² + 25 = (5sqrt(2))²
25×2/4 + 25 = 25×2
25/2 + 25 = 25×2
25/2 = 25
b. is definitely wrong. no equality.
(5sqrt(2)/2)² + 25 = (10sqrt(3)/3)²
25×2/4 + 25 = 100×3/9
25/2 + 25 = 100/3
3×25/2 + 3×25 = 100
3×25 × 2×3×25 = 100×2
75 + 150 = 200
225 = 200
c. is definitely wrong. no equality.
(5sqrt(3)/3)² + 25 = (10sqrt(3)/3)²
25×3/9 + 25 = 100×3/9
25/3 + 25 = 100/3
25 + 3×25 = 100
25 + 75 = 100
100 = 100
d. is correct.