Question

I'm taking a test and don't know how to solve this problem :')

Answer 1

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

Read more about areas at:

brainly.com/question/24487155

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