In triangle √ÜPQR, with PQ =…

Maths Questions

In triangle ÆPQR, with PQ = 39 cm and PN as the altitude, find the length of PR given that QN = 36 cm and RN = 8 cm.

Answer

17 cm Step-by-step explanation: First, we need to determine the length of PN, the altitude of triangle PQR. Since PN is perpendicular to QR, triangles PNQ and PNR are right triangles. We will apply the Pythagorean theorem: a² + b² = c². Let h be equal to PR, the height. Thus, h² + 36² = 39². This simplifies to h² + 1296 = 1521. By subtracting 1296 from both sides, we get h² = 225. Taking the square root results in h = 15 cm. Next, we utilize this height and the base RN to find PR: 15² + 8² = x², which gives us 225 + 64 = x², resulting in 289 = x². Therefore, ,(289) = ,(x²), thus x = 17.

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