Question

Find the area of a rhombus one side of which measures 20 cm and one of whose diagonals is 24 cm.

Solution

Let ABCD is a rhombus with the diagonals AC and BD which intersect each other at O. Given AC = 24cm. Then AO = 12cm. Let BO = x and AB = 20cm. By Pythagoras theorem, we know that  c2=a2+b2 ⇒202=122+x2 ⇒400=144+x2 ⇒x2=400−144 ⇒x2=256 x = 16cm. Diagonal BD = 2 * 16                       = 32cm. We know that Area of the rhombus = 1/2 * (product of diagonals)                                                             = 1/2 * 24 * 32                                                             = 12 * 32                                                             = 384 sq.cm.   MathematicsSecondary School Mathematics IXStandard IX

Suggest Corrections

1

Similar questions
View More

Same exercise questions
View More

People also searched for
View More