Question

Construct triangle QRS if QS = 12cm, angle SQR measures 90 degrees and QR = 6cm answer

A. 1 triangle
B. 2 triangle
C. No triangle
D. 3 triangle​

Answer 1

Given the dimensions QS = 12cm, SQR = 90 degrees, and QR = 6cm, by applying the Pythagorean theorem, only one right-angled triangle QRS can be constructed. Hence, the answer is A. 1 triangle.

Step-by-step explanation:

To construct triangle QRS with QS = 12cm, angle SQR measuring 90 degrees, and QR = 6cm, we can determine the number of possible triangles that can be constructed with these measurements. Given that angle SQR is a right angle, we are dealing with a right-angled triangle. Using the Pythagorean theorem, we can find the length of side RS:

RS² = QS² - QR²
RS² = 12² - 6²
RS² = 144 - 36
RS² = 108
RS = √108
RS = 10.39cm (approx).

With the lengths of all sides determined, we can conclude that there is only one way to construct triangle QRS with the given dimensions. Therefore, the answer to the question is A. 1 triangle.