Answer:
120 square units
Step-by-step explanation:
In triangle PSQ, PS=SQ. Let PS=SQ=x units.
Since SQ-PQ=1, PQ=SQ-1=x-1 units.
The perimeter of the triangle PSQ is 50 units, so
PS+SQ+PQ=50 units.
Substitute PS=SQ=x un. and PQ=x-1 un.
x+x+x-1=50
3x=51
x=17
Hence
PS=SQ=17 units,
PQ=16 units.
Use Heron's formula to find the area:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]
where p is semi-perimeter and a,b,c are lengths of sides.
[tex]p=\dfrac{17+17+16}{2}=25,\\ \\\\A=\sqrt{25(25-17)(25-17)(25-16)}=\sqrt{25\cdot 8\cdot 8\cdot 9}=5\cdot 8\cdot 3=120\ un^2.[/tex]
