The triangle PSQ is an isosceles triangle, and the area of the triangle PSQ is 1360.62 square units
How to determine the area?
The given parameters are:
PS = SQ
Perimeter, P = 50
SQ - PQ = 1
The perimeter is calculated using:
PS + SQ + PQ = 50
This gives
2SQ + PQ = 50
Make SQ the subject in SQ - PQ = 1
SQ = 1 + PQ
So, the equation 2SQ + PQ = 50 becomes
2(1 + PQ) + PQ = 50
Expand
2 + 2PQ + PQ = 50
Evaluate like terms
3PQ = 48
Divide by 3
PQ = 16
Substitute PQ = 16 in SQ - PQ = 1
SQ - 16 = 1
So:
SQ = 17
The area is then calculated using:
A = √[P * (P - PS) * (P - SQ) * (P - PQ)]
This gives
A = √[50 * (50 - 17) * (50 - 17) * (50 - 16)]
Evaluate
A = 1360.62
Hence, the area of the triangle PSQ is 1360.62 square units
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