Posted by Mary on Friday, February 11, 2011 at 5:32pm.
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.
- Math - helper, Friday, February 11, 2011 at 6:02pm
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
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