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sertanlavr [38]
3 years ago
8

Find the height of a paralleogram, if its area is 84square inches, its base is 12 inches, and its height is respresented by x +

2.

Mathematics
2 answers:
Ghella [55]3 years ago
4 0
Hope you are having clear concept on this.

pentagon [3]3 years ago
3 0

\boxed {\text {Area of Parallelogram  = base } \times \text{height}}

<u>Given area = 84 in², base = 12 in and height = (x + 2) in:</u>

12 (x + 2) = 84

-

<u>Find x:</u>

12 (x + 2) = 84

12x + 24 = 84

12x = 84 - 24

12x = 60

x = 5 inches

-

<u>Find height:</u>

Height = x + 2 = 5 + 2 = 7 inches

-

Answer: Height = 7 inches

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Hence AD = DG (Side length of isosceles triangle)

The bisector of ∠ADG is parallel to BH and will bisect AG at point Q

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\angle GAB = cos^{-1} \left (\dfrac{36}{39}  \right )

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GH = 13 in.

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∠DAB = 2 × 22.62° = 45.24°

The height of the parallelogram = AD × sin(∠DAB) =  13 × sin(45.24°)

The height of the parallelogram = 120/13 =  9.23 in.

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