Question

The area of a right triangle is 270 square meters. The height of the right triangle is 15 meters.

What is the length of the hypotenuse of the right triangle?

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m

Answer 1

To solve this, we find the measure of the base using the the formula for the area of a triangle. Then plug both of these into the Pythagorean theorem to solve for the hypotenuse.

Area of a triangle = 1/2 * base * height
270 = 1/2 * 15 * base
270 = (15 / 2)(base)
270(2 / 15) = base
540 / 15 = base
36 = base

Now, we plug into the Pythagorean Theorem of a² + b² = c² where a and b are the legs of the triangle (AKA the base and height) and c is the hypotenuse.

15² + 36² = c²
225 + 1296 = c²
1521 = c²
√c² = √1521
c = √1521
c = 39

The length of your hypotenuse is 39 meters. 

Answer 2

In a right angle triangle the length of the square of the hypotenuse is equal to the sum of the square of the other two side.The length of the hypotenuse of the right triangle is 39 meters.

Given information-

The area of a right triangle is 270 square meters.

The height of the right triangle is 15 meters.

Area of triangle-

Area of the triangle is half of the product of height and base. Thus,

$A=\dfrac{1}{2} \times h\times b$

Put the values,

$270=\dfrac{1}{2} \times 15\times b$

Solve for b,

$b=\dfrac{270\times2}{15}$

$b=36$

Thus the length of the base of the right triangle is 36 meter.

What is Pythagoras theorem?

Pythagoras theorem states that in a right angle triangle the length of the square of the hypotenuse is equal to the sum of the square of the other two side.

Suppose the hypotenuse is x meter long. Thus,

$x^2=15^2+36^2\\x^2=225+1296\\x=\sqrt{1521} \\x=39$

Hence the length of the hypotenuse of the right triangle is 39 meters.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/12306722