# Math

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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 -

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

• Math -

The ratio between the area and the perimeter of a rectangular sheet of paper is 7:5.if the area of the sheet is 38.5cmÂ² find its perimeter

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