The area of a right triangle with one leg measuring 5 ft. and hypotenuse measuring 13 ft. is

First, solve for the other leg. After using the Pythagorean Theorem, we found out that the other leg is 12ft.

Therefore,

Area = (Base x Height)/2
A = (5ft.x 12ft.)/2 = 30 ft. ^2

The area of the triangle is 30 square feet.

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ikarus ikarus · Answer 2 · 2019-07-03T03:15:58+02:00

Answer:

The area of the right triangle is 30 square feet.

Step-by-step explanation:

Give: In a right triangle one leg measures 5 ft and hypotenuse is 13 ft.

We need to find the other leg of the right triangle. We use the Pythagorean statement to find the other leg.

The Pythagorean theorem states the sum of the squares of legs is equal to the square of the hypotenuse.

Let x be the measure of other leg.

So, x^2 + 5^2 = 13^2

x^2 + 25 = 169

Subtract 25 from both sides, we get

x^2 + 25 - 25 = 169 - 25

x^2 = 144

Taking square root on both sides, we get

x = [tex]\sqrt{144}[/tex]

x = 12

The measure of the missing leg is 12 ft.

Now let's find the area of the right triangle.

Area of a right triangle = 1/2*base*height.

Here base =5 and height = 12

Area of the triangle = 1/2*5*12

= 1/2*60

= 30 square feet.