# Thread: Help me with thisㅠㅠ(right triangles)

1. ## Help me with thisㅠㅠ(right triangles)

Find the sides of the [30-60-90] right triangle.
1.hypotenuse=?
shorter leg= ?
longer leg= 12
2. hypotenuse=7√3
shorter leg=?
longer leg=?
3. hypotenuse=?
shorter leg=?
longer leg=15
4. hypotenuse=2√2
shorter leg=?
longer leg=?
5. Find the perimeter of a square if a diagonal is 12.
6. Find the perimeter of an equilateral trianle if an altitude has length 7√3.

Please explain me about how to solve the square root number like 8√3 x 2√2. and 6 x √3.
Thank you...^^
Hope you a lucky day~!!!!!!!!!!

2. Originally Posted by sarayork

Find the sides of the [30-60-90] right triangle.
1.hypotenuse=?
shorter leg= ?
longer leg= 12
2. hypotenuse=7√3
shorter leg=?
longer leg=?
3. hypotenuse=?
shorter leg=?
longer leg=15
4. hypotenuse=2√2
shorter leg=?
longer leg=?
5. Find the perimeter of a square if a diagonal is 12.
6. Find the perimeter of an equilateral trianle if an altitude has length 7√3.
Hello,

I assume that you are referring to degrees here: "...[30-60-90] right triangle".

With such a right triangle the ratio of shorter leg to hypotenuse is : $\frac{l_s}{h}=\frac12$

Use this formula and the Pythagorean theorem to calculate the missing values:

to #1: $l_s=\frac12 \cdot h$ Solve the equation

$h^2 = \left(\frac12 \cdot h \right)^2 + 12^2$ for h and afterwards calculate the shorter leg.

The following questions have to be done similarly.

to #5:

If the side of the square is a and the diagonal is d you find:

$d^2 = a^2+a^2 = 2a^2$ . Use this property to calculate the length of one side and afterwards the perimeter: $p = 4 \cdot a$

to #6:

The altitude of an isosceles triangle with the side a is calculated by: $h=\frac12 \cdot a \cdot \sqrt{3}$.

Plug in the known value of h and solve for a. Afterwards calculate the perimeter: $p = 3 \cdot a$