The area of a quadrilateral is 1470 square centimeters and the length of one of its diagonals is 42 centimetres. Calculate the sum of the lengths of the perpendiculars to this diagonal from the opposite vertices.

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Solution

Area of the quadrilateral = 1470

Length of the diagonal, d = 42 cm

Let the length of the first and the second perpendiculars be p₁ and p₂respectively.

Area of the quadrilateral =

Therefore, the sum of the lengths of the perpendiculars to the given diagonal from the opposite vertices is 70 cm.

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The area of a quadrilateral is 1470 square centimeters and the length of one of its diagonals is 42 centimetres. Calculate the sum of the lengths of the perpendiculars to this diagonal from the opposite vertices.

Area of the quadrilateral = 1470 Length of the diagonal, d = 42 cm Let the length of the first and the second perpendiculars be p1 and p2 respectively. Area of the quadrilateral = Therefore, the sum of the lengths of the perpendiculars to the given diagonal from the opposite vertices is 70 cm.