Question

in right triangle RST altitude TV is drawn to hypotenuse RS If RV = 12 and RT = 18, what is the length of SV

Answer 1

To find the length of SV, use the concept of similar triangles and set up a proportion. The length of SV is (4 / 7) times the length of RS.

Step-by-step explanation:

To find the length of SV, we can use the concept of similar triangles. In right triangle RST, TV is drawn perpendicular to hypotenuse RS. Since TV is an altitude, it divides the hypotenuse into two segments, RT and ST. We are given that RV = 12 and RT = 18. Using the property of similar triangles, we can set up the following proportion:

(RV / RT) = (SV / ST)

Substituting the known values, we get (12 / 18) = (SV / ST). Cross multiplying, we have 12 * ST = 18 * SV. Solving for SV, we get SV = (12 * ST) / 18. Since ST + SV = RS, we can substitute ST with RS - SV. Therefore, SV = (12 * (RS - SV)) / 18. Solving for SV, we get SV = 4(SV - RS) / 3. Further simplifying, we get 7SV = 4RS. Finally, SV = (4 / 7) * RS.

Answer 2

12

Step-by-step explanation:

Given that:

RV = 12 and RT = 18

Kindly refer to attachment for triangle diagram:

Using the altitude on hypotenus theorem :

Length of RS = 12 + a

RT² = RV * RS

18² = 12 * (12 + a)

324 = 12(12 + a)

324 = 144 + 12a

324 - 144 = 12a

180 = 12a

Divide both sides by 12

180/12 = a

15 = a

Hence, SV = 12