Final answer:
To find RT in the isosceles triangle RST, we apply the Pythagorean theorem. The length of each side RS and ST is 6 cm (same as QR, since PQRS is a rectangle). Calculating RT as the base of the right triangle gives us a length of 6√2 cm, which is not reflected in the provided options, implying a possible typo.
Step-by-step explanation:
You are required to find the length of RT in a rectangle PQRS where PS = 10 cm, QR = 6 cm, and T is a point on PQ. Given that RST is an isosceles triangle with RS and ST as its equal sides, we can deduce the length of RT using Pythagoras' theorem.
Since RST is isosceles with RS and ST as equal sides, and given RS = QR (because PQRS is a rectangle), the lengths of RS and ST are both 6 cm. For triangle RST, RT will be the base and can be found by applying the Pythagorean theorem (base^2 = height^2 + height^2).
Here, the height is 6 cm for both RS and ST. So the equation becomes RT^2 = 6^2 + 6^2, which simplifies to RT^2 = 36 + 36, and thus RT^2 = 72. Taking the square root of both sides, RT is equal to the square root of 72, which simplifies to 6√2 cm. However, this does not match any of the options provided. Typo alert: There seems to be a typo in the statement PS is mentioned twice with two values, this need to be clarified.