Question

it is given that the area of a quadilateral is 360m².If the lengths of the perpendicular from the opposite vertices to its diagnols are 10 m and 14 m , find the length of that diagonal​

Answer 1

Answer :—

Length of The Diagonal = 30.

Explanation :—

$\longmapsto\frac{1}{2} \times d \: \times \: (h1 \: + \: h2) \\ \\ \longmapsto360 \: \times \: \frac{1}{2} \times \: d \: \times \: (10 + 14)\\ \\ \longmapsto360 \times 2 = d \: (24) \\ \\ \longmapsto720 \: = \: d \: (24)\\ \\ \longmapsto \frac{720} {24} = \: d \\ \\\longmapsto d \: = 30$

Hence, The Length of The Diagonal = 30 m .

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Answer 2

Given :-

• Area of a quadrilateral = 360 m²

• Length of the perpendiculars = 10 m and 14 m

To Find :-

• Length of the diagonal.

Solution :-

Let the length of the diagonal be "x"

Area of the quadrilateral :-

→ 1/2 × Diagonal × Sum of perpendicular from opposite vertices.

→ 1/2 × x × (10+14) = 360

→ 24x = 720

→ x = 720/24

→ x = 30 cm

∴ Diagonal of the quadrilateral = 30 cm.