The area of a right triangle is 336 cm². The base of the right triangle is 48 cm.
What is the length of the hypotenuse of the right triangle?
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To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
So, we can use the formula:
c² = a² + b²
In this case, the area of the right triangle is given as 336 cm², and the base (a) is given as 48 cm.
We can find the height (b) of the triangle using the formula for the area of a triangle, which is 1/2 * base * height. So:
336 = 1/2 * 48 * height
336 = 24 * height
height = 336 / 24
height = 14 cm
Now we have the values for a and b, so we can substitute them into the Pythagorean theorem:
c² = 48² + 14²
c² = 2304 + 196
c² = 2500
Taking the square root of both sides, we get:
c = √2500
Calculating the square root of 2500, we find:
c ≈ 50 cm
Therefore, the length of the hypotenuse of the right triangle is approximately 50 cm.
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
In this case, we are given the area and the base of the right triangle. The formula for the area of a right triangle is:
Area = (1/2) * base * height
We can rearrange this formula to solve for the height:
height = (2 * Area) / base
Substituting the given values:
height = (2 * 336) / 48
height = 14 cm
Now, we have the length of the two legs of the right triangle (the base and the height). Using the Pythagorean theorem, we can find the length of the hypotenuse:
hypotenuse² = base² + height²
hypotenuse² = 48² + 14²
hypotenuse² = 2304 + 196
hypotenuse² = 2500
Taking the square root of both sides, we get:
hypotenuse = √2500
hypotenuse = 50 cm
Therefore, the length of the hypotenuse of the right triangle is 50 cm.
draw it :)
then draw two more sides to make it into a rectangle
336 is the area of half that rectangle of length x and width h:
(1/2)(48) x = 336
and then
x^2 + 48^2 = hypotenuse^2
The hypotenuse is of course a diagonal of that rectangle you drew.
h^2 + 48^2