Question

Triangle Q S R is shown. Angle Q S R is a right angle. Altitude s is drawn from point S to point T on side Q R to form a right angle. Side Q S is labeled r and side W R is labeled q. The length of Q T is 10 and the length of R T is 4. What is the value of q? 4 StartRoot 5 EndRoot 2 StartRoot 14 EndRoot 20 StartRoot 5 EndRoot 64 StartRoot 5 EndRoot

Answer 1

Answer:

2 square root of 14

Step-by-step explanation:

I was guessing and checking.

Answer 2

The value of q is $2\sqrt{14}$.

Given :

∠QSR = 90°

QS= r , WR = q.

QT = 10 , RT = 4

To find :

The value of q.

Solution:

To determine the value of q, apply the leg rule/geometric mean theorem, which is:

Hypotenuse/leg = leg/part

Hypotenuse = 10 + 4 = 14

Leg = q

Part = 4

Plug in the values into the equation:

$14/q = q/4$

Cross multiply

$q*q = 14*4\\q^2 = 56\\q = \sqrt{56} \\q = \sqrt{4*14} \\q = 2\sqrt{14}$

Therefore, the value of q is $2\sqrt{14}$.

#SPJ3