Question

in triangle XYZ <XYZ=90* XP=PZ,XY=14CM YZ=8.5CM find the area of triangle XYP

Answer 1

area of triangle = 1/2 base × height
so....1/2×14×8.5
7×8.5
59.5

Answer 2

Answer: 57.33 cm²

Step-by-step explanation:

Since, in the right triangle XYZ,

∠ XYZ = 90°, XY=14 cm YZ=8.5 cm,

Thus, by the Pythagoras theorem,

(XZ)² =  (XY)² + (YZ)²

⇒ (XZ)² = 14²  + 8.5² = 196 + 72.25 = 268.25

⇒ XZ = 16.3783394 cm ≈ 16.38 cm,

Hence, the area of the triangle XYZ,

= 1/2 × XY × XZ

= 1/2 × 14 × 16.38 = 7 × 16.38 = 114.66 cm²

Since, P is the mid point of the side AX ( Because, XP=PZ ),

Thus, YP is the median of the triangle XYZ,

By the property of the median,

Area of the triangle XYP = 1/2 of the area of the triangle XYZ

= 1/2 of 114.66

= 57.33 cm²