Question

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The lengths of the sides of a right triangle are a and b, and the hypotenuse is c. Find the area of the triangle.




A = sq. ft.

Answer 1

The area of the triangle is $2\sqrt{3}$ = 3.4641 square feet.

Step-by-step explanation:

Step 1:

According to the Pythagorean theorem, the square of the hypotenuse will be equal to the sum of the squares of the other two sides.

In the given triangle, the hypotenuse is the side that is represented by c. The other sides on the triangle are represented by the values a and b.

Step 2:

Assume the other side of the triangle measures x units.

So according to the Pythagorean theorem,

$4^{2} = (2\sqrt{3} )^{2} + x^{2} , x^{2} = 4^{2} - (2\sqrt{3} )^{2} .$

$x^{2} = 16 - 12 =4, x =2.$

So the other side of the triangle, b measures 2 feet.

Step 3:

The area of a triangle is half the product of its base length and height.

The base length of this triangle is $2\sqrt{3}$ feet and the height is 2 feet.

The area of the triangle$= \frac{1}{2} (2\sqrt{3} )(2) = 2\sqrt{3} = 3.4641.$

The area of the triangle is $2\sqrt{3}$ = 3.4641 square feet.