I have a right triangle whose base is P, whose lay off side is five, and whose hypotenuse is P plus one. Solve for P.

To solve for P in the right triangle using the Pythagorean theorem, we derived the equation and found P to equal 12. This was verified by ensuring that the sides satisfied the theorem. Thus, the value of P is 12.
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Answered by Anonymous | 2025-07-08

To solve for P in a right triangle where the base is P , one leg (lay off side) is 5, and the hypotenuse is P + 1 , you can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse c is equal to the sum of the squares of the other two sides a and b :
a 2 + b 2 = c 2
In this problem:

a = P (the base)
b = 5 (one leg)
c = P + 1 (the hypotenuse)

Now substitute these values into the Pythagorean Theorem:
P 2 + 5 2 = ( P + 1 ) 2
Simplify and solve the equation:

P 2 + 25 = ( P + 1 ) 2

Expand the right side: ( P + 1 ) 2 = P 2 + 2 P + 1

Substitute back: P 2 + 25 = P 2 + 2 P + 1

Cancel P 2 from both sides:
25 = 2 P + 1

Subtract 1 from both sides:
24 = 2 P

Divide both sides by 2 to solve for P :
P = 12


Therefore, the value of P is 12.

Answered by MasonWilliamTurner | 2025-07-22