Mathematics
Littleone44
19

Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long. The height is 6 inches longer than twice the base length. What is the height of the pennant? Recall the formula A = 1/2bh. A.) 12 inches B.) 15 inches C.) 30 inches D.) 36 inches

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(2) Answers
latinaberryhill

A = 1/2 * b * h A = 180 b = z h = 2z + 6 180 = 1/2 * z * 2z + 6 180 = (2z^2 + 6z)/ 2 180 = z^2 + 3z) z^2 + 3z - 180 = 0 (z - 12)(z + 15) = 0 z - 12 = 0 z = 12 z + 15 = 0 z = -15....not this one because it is negative h = 2z + 6 h = 2(12) + 6 h = 24 + 6 h = 30 inches <====

TrinidadDirollo553

The formula for area of a triangle = BH / 2 In which the area = 180 square inches. You can therefore make this formula: 180 = [2(2z+6)+6](2z+6) / 2 Now solve for z. 360 = [2(2z+6)+6](2z+6) 360 = (4z+12+6)(2z+6) 360 = (4z+18)(2z+6) 360 = 8z^2 + 24z + 36z + 108 360 = 8z^2 + 60z + 108     0 = 8z^2 + 60z - 252 Now we will use quadratic formula to get z = 3, -21/2 Substitute in now 2(2z+6) + 6 2(2(3)+6) + 6 2(6+6) + 6 2(12) + 6 24 + 6 30 or... (false) 2[2(-10.5)+6]+6 2(-21+6)+6 2(-15) + 6 -30 + 6 -24 Therefore, the height is 30 inches. I made some work errors but it is still true because of the property ab = ba

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