Answer:
Option B is correct.
Value of x is 15 units.
Step-by-step explanation:
Given: Side ST = 9 units , TQ =16 units and SR = x units.
then, SQ = ST + TQ = 9 + 16 =25 units.
An altitude is drawn from the right angle of a right triangle, then the two triangles formed are similar to the original triangle, then all three triangles are similar to each other.
then,
ΔRTS [tex]\sim[/tex] ΔSRQ.
Lets separate the triangle to find the corresponding sides as shown in figure;
Let us set up a proportion.
[tex]\frac{x}{25} = \frac{9}{x}[/tex]
Simplify:
[tex]x^2 = 25 \times 9[/tex] or
[tex]x = \sqrt{25 \times 9} = 5 \times 3 =15[/tex] units
Therefore, the value of x is 15 units.
