Question

The area of rhombus is 144cm² and one of its diagonals is double the other. The length of the longer diagonal is.​

Answer 1

Step-by-step explanation:

Consider Rhombus ABCD with long diagonal AC and short diagonal BD.

Area is 144cm^2 and the diagonals intersect at E.

EC =1/2AC and ED=1/2BD

Arbitrarily choose any of the 4 triangles bounded by ABCD hiving a right vertex at E. They are all congruent

I chose triangle DEA. Area of which is 1/2(ED x EC)= 36 or 1/4 total area of rhombus.

If EC =2ED then 1/2(ED)(2ED)= 36 and ED=6

Therefore BD= 12 and AC=24cm.

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