Question

THE BASE AND THE CORRESPONDING ALTITUDE OF A PARALLELOGRAM ARE 10CM AND 12 CM RESPECTIVELY.IF THE OTHER ALTITUDE IS 8CM,FIND THE LENGTH OF THE OTHER PAIR OF PARALLEL SIDE........PLEASE HELP...

Answer 1

THE BASE AND THE CORRESPONDING ALTITUDE OF A PARALLELOGRAM ARE 10CM AND 12 CM RESPECTIVELY. IF THE OTHER ALTITUDE IS 8CM, FIND THE LENGTH OF THE OTHER PAIR OF PARALLEL SIDE

Let AB=10 cm, BK=12 cm, BN=8 cm.

Take a look at triangles $\Delta ABD$ and $\Delta CDB$ . They are equal (AB=CD, AD=CB, BD). It means that their areas are equal too.

$$S _ {\Delta A B D} = \frac {1}{2} \cdot A D \cdot B D = \frac {1}{2} \cdot 1 2 \cdot 1 0 = 6 0 c m ^ {2}$$ $$S _ {\Delta C D B} = \frac {1}{2} \cdot B N \cdot C D = \frac {1}{2} \cdot 8 \cdot C D = 4 C D$$ $$S _ {\Delta C D B} = S _ {\Delta A B D}$$ $$4 C D = 6 0, \quad C D = B A = \frac {6 0}{4} = 1 5 c m.$$