Mathematics
28.12.2021 20:21
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Kyla makes a triangular school pennant. The area of the triangle is 180 square inches.

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 = bh.
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keigleyhannah30
keigleyhannah30
4,8(99 marks)

Height of the pennant is 30 inches.

Step-by-step explanation:

Given that:

Area of pennant = 180 sq inches

Base of pennant = z inches

Height of pennant = (2z + 6) inches

Also, it is a triangular pennant and area of a triangle can be given as:

A = \dfrac{1}{2}  \times Base\times Height

Putting the values in above formula:

180 = \dfrac{1}{2} \times z \times (2z+6)\\\Rightarrow 360 = 2z^{2} + 6z\\\Rightarrow 180 = z^{2} + 3z\\\Rightarrow z^{2} + 3z -180 = 0\\\Rightarrow z^{2} + 15z -12z -180 = 0\\\Rightarrow z(z + 15) -12(z+15) = 0\\\Rightarrow (z + 15) (z-12) = 0\\\Rightarrow z = 12\ or\ z=-15

Value of z can not be negative, so value of Base, z = 12 inches.

Height is given as 2z + 6 so, height = 2\times12 +6 = 30 inches

rhineharttori
rhineharttori
4,7(77 marks)

The answer is B, or the second option: The sequence is recursive and can be represented by the function f(n + 1) = f(n) + f of n plus 1 equals f of n plus StartFraction 3 Over 8 EndFraction..

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