Question

I
Q31 If the sum of p/q and its reciprocal is 1 (p and q not equal to 0), then the value of p+2 is:
Ops: A. 03
B. O2
OO
01
of the latest triangle that can be inscribed In a semi-circle of radius "r" units is:​

Answer 1

Answer:

B.02.

will be the correct answer......

Answer 2

Answer:

This perpendicular bisects the base and is also the height of the triangle. The area of the triangle is given by:

(area) = 1/2 x base x height

= 1/2 x 2r x (r)

= r^2

Therefore, the area of the inscribed triangle is r^2, which is the largest possible area for a triangle inscribed in a semi-circle of radius "r" units.

Explanation:

To solve the given problem, we need to use algebraic manipulation and solve for the value of p+2 given the condition that the sum of p/q and its reciprocal is 1.

Let's begin by writing the expression for the sum of p/q and its reciprocal:

p/q + q/p = 1

We can simplify this expression by multiplying both sides by pq:

p^2 + q^2 = pq

Now, let's rearrange this expression to isolate p:

p^2 - pq + q^2 = 0

Using the quadratic formula, we can solve for p:

p = [q ± sqrt(q^2 - 4q^2)]/2

Simplifying the expression under the square root:

p = [q ± sqrt(-3q^2)]/2

As p and q are not equal to 0, we can conclude that the expression under the square root is negative, so there is no real solution for p. Therefore, none of the given options (A. 03, B. O2, OO, 01) is the correct answer.

Regarding the second part of the question about the largest triangle that can be inscribed in a semi-circle of radius "r" units, we can solve it as follows:

We know that the diameter of the semi-circle is equal to 2r, which is also the base of the inscribed triangle. We can draw a perpendicular from the center of the semi-circle to the midpoint of the base, which divides the base into two equal parts of length r each.

This perpendicular bisects the base and is also the height of the triangle. The area of the triangle is given by:

(area) = 1/2 x base x height

= 1/2 x 2r x (r)

= r^2

Therefore, the area of the inscribed triangle is r^2, which is the largest possible area for a triangle inscribed in a semi-circle of radius "r" units.

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