Question
A triangle inside a rectangle has a leg of 208 m, a left side of 105, the hypotenuse is 233, what is the area of the rectangle?
Answers
Answered by
GPT 3.5
To find the area of the rectangle, we first need to determine the height of the triangle inside the rectangle. This can be done using the Pythagorean theorem:
a^2 + b^2 = c^2
Where a and b are the legs of the triangle and c is the hypotenuse. In this case, one leg is 105m and the hypotenuse is 233m:
105^2 + b^2 = 233^2
11025 + b^2 = 54289
b^2 = 43264
b = √43264
b = 208m
Now that we have the height of the triangle, we can find the area of the rectangle:
Area = base * height
Area = 105m * 208m
Area = 21840 sqm
Therefore, the area of the rectangle is 21840 square meters.
a^2 + b^2 = c^2
Where a and b are the legs of the triangle and c is the hypotenuse. In this case, one leg is 105m and the hypotenuse is 233m:
105^2 + b^2 = 233^2
11025 + b^2 = 54289
b^2 = 43264
b = √43264
b = 208m
Now that we have the height of the triangle, we can find the area of the rectangle:
Area = base * height
Area = 105m * 208m
Area = 21840 sqm
Therefore, the area of the rectangle is 21840 square meters.