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.

2. 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. $\left(5 \cdot \sqrt{3}\right)$