a rectangle is to be inscribed in a isosceles triangle of height 8 and base 10. Find the greatest area of such rectangle.
test
To find the greatest area of a rectangle inscribed in an isosceles triangle, we need to determine the dimensions of the rectangle.
Step 1: Understand the problem.
In this case, we have an isosceles triangle with a height of 8 and a base of 10. The rectangle is inscribed in the triangle, meaning it will touch the triangle at all four sides.
Step 2: Determine the dimensions of the rectangle.
To maximize the area of the rectangle, it needs to be as large as possible while still being completely inside the triangle. The rectangle will have two sides parallel to the base of the triangle and two sides parallel to the height of the triangle.
Step 3: Calculate the dimensions.
The base of the rectangle will be equal to the base of the triangle, which is 10 in this case. The height of the rectangle will be equal to the height of the triangle, which is 8.
Therefore, the dimensions of the rectangle are: base = 10 and height = 8.
Step 4: Calculate the area of the rectangle.
To calculate the area of a rectangle, multiply its base by its height.
Area = base * height = 10 * 8 = 80.
Therefore, the greatest area of the rectangle inscribed in the isosceles triangle is 80 square units.
To find the greatest area of a rectangle inscribed in an isosceles triangle, we need to determine the dimensions of the rectangle and calculate its area.
Let's start by drawing a diagram:
```
/\
/ \
/ \
/______\
```
In this triangle, the altitude (height) is given as 8 units, and the base is 10 units.
To find the greatest area of the inscribed rectangle, we want to maximize the dimensions of the rectangle inside the triangle.
Upon observing the given triangle, we can see that the rectangle will have its base aligned with the base of the triangle, and its height will be equal to the altitude of the triangle.
Thus, the base of the rectangle will also be 10 units, and its height will be 8 units.
The area of a rectangle is calculated by multiplying its length (base) by its width (height):
Area = length × width
Area = 10 units × 8 units
Area = 80 square units
Therefore, the greatest area of the rectangle inscribed in the isosceles triangle is 80 square units.