A triangle inside a rectangle has a leg of 156m, a hypotenuse of 175m, and a right side of 79m, what is the area of the rectangle

Answer 1

To find the area of the rectangle that contains the triangle, we need to find the dimensions of the rectangle first.

Since the triangle is inside the rectangle, the leg of 156m is the width of the rectangle and the right side of 79m is the height of the rectangle.

Now, let's find the length of the rectangle:

Using the Pythagorean theorem:
\(a^2 + b^2 = c^2\),
where a = 156m and c = 175m (hypotenuse of the triangle)

\(156^2 + b^2 = 175^2\),
\(b^2 = 175^2 - 156^2\),
\(b^2 = 30625 - 24336\),
\(b^2 = 6291\),
\(b = \sqrt{6291}\),
\(b ≈ 79.4m\)

Therefore, the length of the rectangle is approximately 79.4m.

Now, calculate the area of the rectangle:
Area = width x length,
Area = 79m x 156m,
Area = 12324 square meters.

So, the area of the rectangle that contains the triangle is 12324 square meters.