In triangle pqr qx perpendicular pr and py perpendicular qr. if pq10cm qr8cm and pr5.6cm find the length of py where qx 7.2cm?

Answer 1

There is a problem with your question:

If pq = 10 cm, qr = 8 cm and pr = 5.6 cm then if qx is perpendicular to pr through q it does NOT equal 7.2 cm; it is approx 8.0 cm:

Let X be the distance px, then xr = 5.6 - X

Using Pythagoras:

In pxq: 10² = qx² + X² → qx² = 10² - X²

In rxq: 8² = qx² + (5.6 - X)² → qx² = 8² - (5.6 - X)²

→ 10² - X² = 8² - (5.6 - X)²

→ 10² - X² = 8² - 5.6² + 2×5.6×X - X²

→ 2×5.6×X = 10² - 8² + 5.6²

→ X = (10² - 8² + 5.6²)/(2×5.6)

→ qx² = 10² - ( (10² - 8² + 5.6²)/(2×5.6) )²

→ qx = √(10² - ( (10² - 8² + 5.6²)/(2×5.6) )²) ≈ 7.989265 cm ≈ 8.0 cm

Similarly, for py:

py = √(10² - ( (10² - 5.6² + 8²)/(2×8) )²) ≈ 5.59248 cm ≈ 5.6 cm

The obtuse triangle has angles: qpr ≈ 53°, prq ≈ 93°, rqp ≈ 34°; the perpendiculars qx and py lie outside the triangle; angle prq ≈ 93° which is not far off a right angle making sides pr and qr approximately perpendicular, and shows that the perpendiculars to the sides next to it (ie the perpendiculars to pr and qr) will be approximately equal to the lengths of the other side (next to it, ie length of perpendicular to pr will be approx qr, and the length of the perpendicular to qr will be approx pr).