Question

4. The triangle PQS in which QR = 6cm,PS= 18cm and PR = RS =Xcm, Calculate the height PQ. P Q XCM XX R 18см ++ х см S​

Answer 1

To find the height PQ of the triangle PQS, use the Pythagorean theorem and set up equations based on the given measurements. Solve for the height PQ using the equations and find it to be approximately 15.87 cm.

Step-by-step explanation:

To find the height PQ of the triangle PQS, we can use the Pythagorean theorem. Since PR = RS = X, we can use X as the base of the triangle. Let's call the height PQ as h. We can set up the equation:

X^2 = h^2 + 6^2

Substituting the values, we get:

X^2 = h^2 + 36

Since PS = 18, we can also use the Pythagorean theorem for the triangle PSR:

18^2 = X^2 + 6^2

Substituting the value of X^2 from the previous equation, we get:

324 = h^2 + 36 + 36

Simplifying, we have:

h^2 = 324 - 72

h^2 = 252

Taking the square root, we get:

h ≈ 15.87 cm