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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