A brand of crescent rolls are packaged in tubes that contain

A brand of crescent rolls are packaged in tubes that contain perforated triangles of dough. The base of the triangular piece of dough is about 4 centimeters more than its height. Determine the base and height of a piece of dough if the area is about 70 square centimeters.

Solution

Let h be the height of the pieces of dough. Then the base of these triangular pieces of dough is h + 4. We know that the area of the triangle is 1/2( base)* (height). Therefore, 1/2h(h+4) = 70 or h(h +4) = 140 or, h² + 4h - 140 = 0. Therefore, h = [ - (4) ± { ( 4)² – 4 (1)( -140)}]/ 2*1 = [ - 4 ± ( 16+ 560)]/2 = [- 4 ± 576] /2 = (- 4 ± 24)/2. Thus h = (- 4 +24)/2 (as h cannot be negative). Therefore, h = 20/2 = 10cm. Then the base of the piece of dough is h + 4 = 10 + 4 = 14cm.