# If the hypotenuse of a right triangle is 10 and one leg is 5 square root 3, then the area of the triangle is

a. 5
b. 25 square root 3
c. 25
d. 50 square root 3
e. 12.5 square root 3

please answer and explain

## Use Pythagorean theorem to find other leg.

h^2 + b^2 = Hypotenuse^2

h^2 + (5√3)^2 = 100

Solve for h.

Area = 1/2 hb

Insert values and solve for area.

## h^2 + 75 = 100

h^2 = 25
h = 5

5 x 5 square root 3 /2
=25 square root 3 /2
= 12.5 square root 3

answer e

right?

## From the way you have your last equation written "square root 3 /2" Looks like √(3/2).

It should be written (25√3)/2. The brackets make the meaning clearer.

The square root sign (√) can be obtained by using "v" and "alt/option" keys simultaneously.

Otherwise, you are right.

## To find the area of the triangle, we can use the formula for the area of a right triangle: A = (1/2) * base * height.

In this case, the hypotenuse of the triangle is given as 10, which is also the longest side. Let's label the hypotenuse as c, the shorter leg as a, and the longer leg (the one given as 5√3) as b.

Since the hypotenuse is the longest side, it must be the one opposite the right angle. Therefore, it is the side that connects the two legs of the triangle.

We know that one leg (b) is given as 5√3. Let's find the value of the other leg (a).

Using the Pythagorean theorem, we can find the value of a:

a^2 + b^2 = c^2
a^2 + (5√3)^2 = 10^2
a^2 + 75 = 100
a^2 = 100 - 75
a^2 = 25

Taking the square root of both sides, we find that a = 5.

Now that we know both the legs of the triangle (a = 5 and b = 5√3), we can find the area of the triangle using the formula:

A = (1/2) * a * b
A = (1/2) * 5 * 5√3
A = (1/2) * 25√3
A = 12.5√3

Therefore, the area of the triangle is option e: 12.5√3.