According to the HL theorem if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle then the triangles are congruent.

By using this theorem we can set up the system of equations as follows:

x=y+1 ...(1)

2x+3= 3y + 3 ..(2)

Now we will plug the value y+1 of equation 1 in equation 2.

2x+3 = 3y+3

2(y+1)+3=3y+3

2y+2+3=3y+3

2y+5=3y+3

Now combine the like terms:

5-3=3y-2y

2=y

y=2

Now plug the value y=2 in equation 1.

x=y+1

x=2+1

x=3

Thus the values of(x.y) are{(2,3)}

Therefore the correct option is x=3 , y=2 .....

3 0

3 years ago

This is the full question

nekit [7.7K]

Given: cos A = 5/13 = adj side / hypotenuse

The the opp side is given by (hypo)^2 = (adj)^2 + (opp)^2. Here,
13^2 = 5^2 + (opp)^2, so that
(opp)^2 = 169 - 25 - 144. Then opp = +12. All of these lengths are in Q I.
opp 12
Then sin A = -------- = -------- (answer)
hyp 13

8 0

3 years ago

There are 3 consecutive integers such that the sum of the 2 smallest integers is 17 less than three times the largest. What is t

RSB [31]

Answer:

X + (X+1) +(X+2)

(X+(X+1)) = 3 *(X+2) + 17

2X +1 = 3X + 6 +17

X = -22

So the three integers are -22 -21 and -20

Double-Check *******************

(-22 -21) = 3 * (-20)

-43 = -60 +17

Step-by-step explanation:

8 0

3 years ago