If P is the orthocenter of △ABC, AB = 13, BF = 9,and FC = 5.6, find each measure & the perimeter of triangle ABC.

Given that P is the orthocenter of triangle ABC, applying the properties of an orthocenter of a triangle and the Pythagorean Theorem, each measure and the perimeter of △ABC are:

AB = 13BC = 10.6AC = 15Perimeter = 38.6

Recall:

An altitude is the line that connects the vertex of a triangle to the opposite side of which it is perpendicular to that side.Orthocenter is the point where all three altitudes intersect each other.

Given that P is the orthocenter of triangle ABC, where,

AB = 13BF = 9FC = 5.6

Perimeter of △ABC = AB + BC + AC

First, we need to find BC and AC.

△BFC is a right triangle, apply Pythagorean theorem to find BC:

Substitute

△BFA is a right triangle, apply Pythagorean theorem to find FA:

Substitute

AC = FA + FC

Substitute

AC = 9.4 + 5.6

AC = 15

Perimeter of △ABC = AB + BC + AC

Substitute

Perimeter of △ABC = 13 + 10.6 + 15

Perimeter of △ABC = 38.6 units

Therefore, given that P is the orthocenter of triangle ABC, applying the properties of an orthocenter of a triangle and the Pythagorean Theorem, each measure and the perimeter of △ABC are:

AB = 13BC = 10.6AC = 15Perimeter = 38.6

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Step-by-step explanation:

Given

Required

Calculate the perimeter of A B C

To calculate the perimeter of A B C, we sum up the sides of the triangle

i.e.

AB is given in the question already.

So, we need to calculate B F and F C

To solve for BF, we consider triangle B F C

Using Pythagoras Theorem, we have:

Substitute values for BF and FC;

Next, we calculate A C.

To calculate A C, we need to calculate A F, considering triangle B F A

Using Pythagoras Theorem, we have:

Substitute values for B F and A B;

Since F lies on line A C:

Recall that:

Hence, the perimeter is 38.6

The answer is C : The area of sector AOB is equal to the area of sector DOC because the central angle measures are equal.

Step-by-step explanation:

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