Thread: If any lovely person would be so kind as to help me out, I'll love them forever.

What is the length of the longer leg of a 30-60-90 triangle with the hypotenuse of length 24 square root of 3 meters squared?

If the area of a square is 225 cm squared, what is the length of the diagonal?

What is the length of the hypotenuse of a right triangle with legs of length 80 ft and 150 feet?

Find the circumference of a circle inscribed in an equilateral triangle with a height of 12 square root of 3 in.

Find the area of an equilateral triangle with sides measuring 6 meters.

Is triangle ABC with vertices A(2,4), B(10,2), and C(7,7) scalene, isosceles, or equilateral?

Originally Posted by Lizi1308

What is the length of the longer leg of a 30-60-90 triangle with the hypotenuse of length 24 square root of 3 meters squared?

The longest side is the hypotenuse.

Originally Posted by Lizi1308

If the area of a square is 225 cm squared, what is the length of the diagonal?

Area = length squared, so the length must be 25. Use this value with pythagoras thm to determine the diagonal

Originally Posted by Lizi1308

What is the length of the hypotenuse of a right triangle with legs of length 80 ft and 150 feet?

Use pythagora's thm, it says, the hypotenuse squared equals the summed squares of the remaining sides.

Originally Posted by Lizi1308

What is the length of the longer leg of a 30-60-90 triangle with the hypotenuse of length 24 square root of 3 meters squared?
If the area of a square is 225 cm squared, what is the length of the diagonal?
What is the length of the hypotenuse of a right triangle with legs of length 80 ft and 150 feet?

These are all simple applications of the Pythagorean Theorem. Look it up if necessary, and If you really can't figure it out, show us what you've tried.

Originally Posted by Lizi1308

Find the circumference of a circle inscribed in an equilateral triangle with a height of 12 square root of 3 in.

Form some line segments connecting the center of the circle to the vertices of the triangle and to the midpoints of its sides. Then you should be able to use the newly-formed right triangles to determine some of the needed lengths. The main thing you're looking for is the radius of the circle, so that you can use your circumference formula.

Originally Posted by Lizi1308

Find the area of an equilateral triangle with sides measuring 6 meters.

Split it into two right triangles. Use the Pythagorean Theorem again.

Originally Posted by Lizi1308

Is triangle ABC with vertices A(2,4), B(10,2), and C(7,7) scalene, isosceles, or equilateral?

To determine what kind of triangle you have, you should start by determining the lengths of the sides. How do you find the distance between two points?

Originally Posted by pickslides

Area = length squared, so the length must be 25. Use this value with pythagoras thm to determine the diagonal

Not quite. I guess you misread that as 625.