An isosceles triangle and a rectangle share a base. The area of the rectangle is 4 times the area of the triangle. The area of the triangle is 60 cm^2 and its height is 15 cm. Find the dimensions of the triangle.
Triangle Area = 1/2 bh
60 = 1/2 15b
120 = 15b
b = 8
base = 8
height = 15
s = sides
The height h of the isosceles triangle
h = (sqrt(s^2 - 1/4 b^2))
15 = (sqrt(s^2 - 1/4 8^2))
15 = (sqrt(s^2 - 1/4 64))
15 = (sqrt(s^2 - 16))
Square both sides
225 = s^2 - 16
s^2 = 241
s = 15.52
Or, you can use the Pythagorean theorem
The height forms two right triangles.
side a = 15
side b = 4 (8/2 = 4)
side c = hypotenuse (side of isosceles)
c^2 = 4^2 + 15^
c^2 = 16 + 225
c^2 = 241
c = 15.52
Dimensions of triangle,
Equal sides = 15.52
base = 8
The ratio between the area and the perimeter of a rectangular sheet of paper is 7:5.if the area of the sheet is 38.5cm² find its perimeter
To find the dimensions of the triangle, we need to first define some variables.
Let's say:
- The base of the triangle is 'b' cm
- The height of the rectangle is 'h' cm
- The length of the rectangle is 'l' cm
We are given that the area of the triangle is 60 cm^2, so we can use the formula for finding the area of a triangle: A = (1/2) * b * h. Plugging in the given values, we can solve for 'b':
60 = (1/2) * b * 15
120 = b * 15
b = 120/15
b = 8 cm
Now that we know the base of the triangle, we can find the length and width of the rectangle. We are given that the area of the rectangle is 4 times the area of the triangle. Since the area of the triangle is 60 cm^2, the area of the rectangle is 4 * 60 = 240 cm^2.
Since the area of a rectangle is given by A = length * width, we have the equation:
240 = l * h
We know that the height of the rectangle is 15 cm, so we can solve for the length of the rectangle:
240 = l * 15
l = 240/15
l = 16 cm
Therefore, the length of the rectangle is 16 cm, and the width is also 15 cm (since it shares the base with the isosceles triangle).
So, the dimensions of the triangle are:
Base: 8 cm
Height: 15 cm