For the rhombus ABCD, diagonal BD = 18 and diagonal AC = 24. What is the side length of the rhombus? A) 15 2 B) 21 2 C) 15 D) 21

1 answer:

8 0

The diagonals are perpendicular to each other.
The right triangle has half of each diagonal as sides, so the hypotenuse or side length is Sqrt(9^2 + 12^2) = 15.
Hint: a 3,4,5 sided triangle is the smallest integer right triangle. Doubling or tripling, etc. is still a right triangle. So when I saw the 9,12, I knew that 15 was the hypotenuse.

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Triangle DEF has vertices D(0,0), E(7,0), and F(3,7).

Leni [432]

Answer:

(3, 1.7)

Step-by-step explanation:

The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.

Two lines are perpendicular if the product of their slopes is -1.

The slope of the line joining D(0,0), F(3,7) is:

$m_1=\frac{7-0}{3-0}=\frac{7}{3}$

The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=-\frac{3}{7} (x-7)\\\\y=-\frac{3}{7}x+3 \ .\ .\ .\ (1)$

The slope of the line joining E(7,0), and F(3,7). is:

$m_1=\frac{7-0}{3-7}=-\frac{7}{4}$

The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=\frac{4}{7} (x-0)\\\\y=\frac{4}{7} x\ .\ .\ .\ (2)$