Question

Given: ΔPSQ, PS = SQ Perimeter of ΔPSQ = 50 SQ – PQ = 1 Find: Area of ΔPSQ

Answer 1

Answer:

  120 units²

Step-by-step explanation:

Perimeter = PS + SQ + PQ

50 = SQ + SQ + (SQ -1)

51 = 3SQ

17 = SQ

17 -1 = 16 = PQ

The midpoint of the base is one leg of the right triangle whose other leg is the height of this isosceles triangle. That height is ...

  h = √(17² -(16/2)²) = √225 = 15

Then the area is ...

  A = (1/2)bh = (1/2)(16)(15) = 120 . . . . . square units