Posted by **Jujube** on Monday, January 21, 2008 at 12:05pm.

1. A rhombus has a perimeter of 96, and the length of one of its diagonals is 32. The area of the circle inscribed in the rhombus can be expressed as k*pi/w where k and w are relatively prime positive integers. Find the value of k + w.

- math PLEASE HELP -
**Reiny**, Monday, January 21, 2008 at 2:19pm
the diagonals of a rhomus bisect each other at right angles, forming 4 equal right-angled triangles

the hypotenuse of each is 96/4 or 24 and one side is 32/2 or 16.

so by Pythagoras, the other side is sqrt(320)

The centre of the incsribed circle is at the intersection of the diagonals, so I drew a height inside one of the triangles.

by some basic geometry I found the r^2 = 1280/9

so the area of the circle is pi*1280/9 but that is given to be k*pi/w

so k*pi/w = pi*1280/9

since 1280/9 is relatively prime, k+w = 1280+9 = 1289

## Answer This Question

## Related Questions

- math-geometry - 1. A rhombus has a perimeter of 96, and the length of one of its...
- easy geometry - 1)If diagonals of a rhombus are 10 cm and 24 cm. find the area ...
- math - The area of a rhombus is 60cm^2. Given that one of its diagonals is 15 cm...
- math - the length of the diagonals of a rhombus are in the ratio 3:4 if one side...
- Math - Which of the following statements is not always true? A. In a rhombus, ...
- geometry - The diagonals of a rhombus are in 2:1. If the perimeter of the ...
- geometry - Which of the following statements is not always true? A. In a rhombus...
- maths - the length of the diagonals of a rhombus are 24cm and 32cm. the ...
- easy GEOMETRY!! - 1.The perimeter of parallelogram QUAD is 10 more than 5 times ...
- geometry - 1.The perimeter of parallelogram QUAD is 10 more than 5 times AU. If ...

More Related Questions