Math, asked by osjshsbsb, 3 days ago

the diagonal of a quadrilateral measures 24cm and the lengths of the perpendiculars drawn to it from opposite vertices is in the ratio 3:2. find the lengths of the perpendiculars,if the area of the quadrilateral

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Answers

Answered by namjinsopevminkook77

Answer:

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$....$

Step-by-step explanation:

Given :

Area of Quadrilateral = 390m²

Diagonal of Quadrilateral = 24cm

Ratio of the two perpendiculars = 3:2

To Find :

The lengths of the perpendiculars.

Solution :

✰ As we know that, Area of Quadrilateral is given by ½ × diagonal × (sum of perpendiculars). Now in this question, Area of Quadrilateral and Diagonal of Quadrilateral along with Ratio of perpendiculars are given. So we will assume the first and second perpendicular as 3x and 2x respectively . After that we will simply put the given values in the formula to find the Perpendiculars of the Quadrilateral.

⠀⠀

⠀⟼⠀⠀Area = ½ × diagonal × (P1 + P2)

⠀⟼⠀⠀390 = ½ × 24 × (3x + 2x)

⠀⟼⠀⠀390 = ½ × 24 × 5x

⠀⟼⠀⠀390 × 2 = 24 × 5x

⠀⟼⠀⠀780 = 24 × 5x

⠀⟼⠀⠀780/24 = 5x

⠀⟼⠀⠀32.5 = 5x

⠀⟼⠀⠀32.5/5 = x

⠀⟼⠀⠀6.5m = x

⠀⠀

Therefore :

⇢ First Perpendicular = 3x

⇢ First Perpendicular = 3 × 6.5

⇢ First Perpendicular = 19.5m

⠀

⇢ Second Perpendicular = 2x

⇢ Second Perpendicular = 2 × 6.5

⇢ Second Perpendicular = 13m

⠀⠀

Thus Perpendicular of the Quadrilateral are 19.5m and 13m respectively.

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