Question

A Rhombus has an area of 40 cm^2 and adjacent angles of 50° and 130°. Find the length of a side of the Rhombus.​

Answer 1

Answer:

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Step-by-step explanation:

Let ABCD be the rhombus whose area is 40 sq cm and not 40 cm as stated.

Let ABCD be the rhombus whose area is 40 sq cm and not 40 cm as stated.Let the diagonals AC and BD intersect at O.

Let ABCD be the rhombus whose area is 40 sq cm and not 40 cm as stated.Let the diagonals AC and BD intersect at O.There are 4 right-angled triangles ABO, BCO, CDO, and DAO all having their area as 10 sq cm. The two angles are 25 and 65 degrees while the third angle is 90 degrees.

Let ABCD be the rhombus whose area is 40 sq cm and not 40 cm as stated.Let the diagonals AC and BD intersect at O.There are 4 right-angled triangles ABO, BCO, CDO, and DAO all having their area as 10 sq cm. The two angles are 25 and 65 degrees while the third angle is 90 degrees.Let each side of the rhombus be x which will be the hypotenuse of each of the 4 triangles. The sides of the triangle, OA (that is, half of each diagonal of the rhombus) = x cos 25 = 0.906307787x and OB = x cos 65 = 0.422618261x.

Let ABCD be the rhombus whose area is 40 sq cm and not 40 cm as stated.Let the diagonals AC and BD intersect at O.There are 4 right-angled triangles ABO, BCO, CDO, and DAO all having their area as 10 sq cm. The two angles are 25 and 65 degrees while the third angle is 90 degrees.Let each side of the rhombus be x which will be the hypotenuse of each of the 4 triangles. The sides of the triangle, OA (that is, half of each diagonal of the rhombus) = x cos 25 = 0.906307787x and OB = x cos 65 = 0.422618261x.Thus the diagonals AC = 2xOA = 1.812615574x and BD = 2xOB = 0.845236523x

Let ABCD be the rhombus whose area is 40 sq cm and not 40 cm as stated.Let the diagonals AC and BD intersect at O.There are 4 right-angled triangles ABO, BCO, CDO, and DAO all having their area as 10 sq cm. The two angles are 25 and 65 degrees while the third angle is 90 degrees.Let each side of the rhombus be x which will be the hypotenuse of each of the 4 triangles. The sides of the triangle, OA (that is, half of each diagonal of the rhombus) = x cos 25 = 0.906307787x and OB = x cos 65 = 0.422618261x.Thus the diagonals AC = 2xOA = 1.812615574x and BD = 2xOB = 0.845236523xThe area of the rhombus = AC*BD/2 = 1.812615574x*0.845236523x/2

Let ABCD be the rhombus whose area is 40 sq cm and not 40 cm as stated.Let the diagonals AC and BD intersect at O.There are 4 right-angled triangles ABO, BCO, CDO, and DAO all having their area as 10 sq cm. The two angles are 25 and 65 degrees while the third angle is 90 degrees.Let each side of the rhombus be x which will be the hypotenuse of each of the 4 triangles. The sides of the triangle, OA (that is, half of each diagonal of the rhombus) = x cos 25 = 0.906307787x and OB = x cos 65 = 0.422618261x.Thus the diagonals AC = 2xOA = 1.812615574x and BD = 2xOB = 0.845236523xThe area of the rhombus = AC*BD/2 = 1.812615574x*0.845236523x/2= 0.766044443 x^2 which is given as 40 sq cm.

Let ABCD be the rhombus whose area is 40 sq cm and not 40 cm as stated.Let the diagonals AC and BD intersect at O.There are 4 right-angled triangles ABO, BCO, CDO, and DAO all having their area as 10 sq cm. The two angles are 25 and 65 degrees while the third angle is 90 degrees.Let each side of the rhombus be x which will be the hypotenuse of each of the 4 triangles. The sides of the triangle, OA (that is, half of each diagonal of the rhombus) = x cos 25 = 0.906307787x and OB = x cos 65 = 0.422618261x.Thus the diagonals AC = 2xOA = 1.812615574x and BD = 2xOB = 0.845236523xThe area of the rhombus = AC*BD/2 = 1.812615574x*0.845236523x/2= 0.766044443 x^2 which is given as 40 sq cm.Therefore, x the side of the rhombus = (40/0.766044442)^0.5 = 7.226084113 cm