• Nov 15th 2007, 01:13 AM
sarayork
1. A rectangle has a diagonal of 2 and length of √3. Find its width.

2. Find the length of a side of a square with a diagonal of lenth 12.

3. The perimeter of a rhombus is 40cm, and one diagonal is 12cm long. How
long is the other diagonal?

3. A diagonal of a square has lenth 8. What is the perimeter of the square?

4. Find the altitude of an equilateral triangle if each side is 10 units long.

• Nov 15th 2007, 02:01 AM
earboth
Quote:

Originally Posted by sarayork
1. A rectangle has a diagonal of 2 and length of √3. Find its width.

2. Find the length of a side of a square with a diagonal of lenth 12.

3. The perimeter of a rhombus is 40cm, and one diagonal is 12cm long. How
long is the other diagonal?

3. A diagonal of a square has lenth 8. What is the perimeter of the square?

4. Find the altitude of an equilateral triangle if each side is 10 units long.

Hello,

to 1.) A rectangle is divided into 2 congruent right triangles by one diagonal. The diagonal is the hypotenuse of the right triangle. If l is the length of the rectangle, w is the width and d is the diagonal then you have the equation:
$d^2 = l^2+w^2$ . Plug in the values you know:

$2^2 = (\sqrt{3})^2 + w^2$ and solve for w. (1)

to 2.) A square is a special rectangle with l = w. Use the formula given above and solve for l:

$12^2 = 2 \cdot l^2$.
$(6\sqrt{2})$

to 3.) A rhombus is divided by the 2 diagonals into 4 congruent right triangles where the side of the rhombus is the hypotenuse.
length of one side: 10
half of the given diagonal: 6

If the half of the other diagonal is e (in Germany usually the diagonals are labeled e and f) then you get:

$10^2 = 6^2 + e^2$ . Solve for e and calculate the complete length. (16)

to 3.) again: If s is the length of one side of the square then the perimeter of a square is $p = 4 \cdot s$. Calcualte the length of one side (same procedure as in #2.) and then the perimeter. $(16\sqrt{2})$

to 4.) An equilateral triangle is divided into 2 congruent right triangles where the side of the triangle is the hypotenuse, one leg is the altitude and the other leg is the half of one side. Let h be the altitude then you have:

$10^2 = 5^2 + h^2$ . Solve for h. $\left(5 \cdot \sqrt{3}\right)$