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  • In Figure, DeltaABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC, a parallelogram, DBCE of same area as that of DeltaABC is constructed. Find the height DF of the parallelogram.

In Figure, △ABC has sides AB=7.5 cm,AC=6.5 cm and BC=7 cm. On base BC, a parallelogram, DBCE of the same area as that of △ABC is constructed. Find the height DF of the parallelogram.

  

Answers (1)

Solution:

AB=7.5 cm,AC=6.5 cm,BC=7 cm

Let a=7.5 cm, b=6.5 cm,c=7 cm
Now, S=a+b+c2=7.5+6.5+72=212=10.5 cm
Area of △ABC,By heron's formula =S(S−a)(S−b)(S−c)

=10.5(10.5−7.5)(10.5−6.5)(10.5−7)=10.5×3×4×3.5

=10510×3×4×3510=21×3×7=3×7×3×7=3×7=21 cm2

Now, we find the length DF of parallelogram DBCE
Area of parallelogram = base × height =BC×DF
Area of parallelogram =7DF
According to the question,
Area of △ABC= Area of parallelogram DBCE

21=7DF217=DFDF=3 cm

Hence the height of the parallelogram is 3 cm.

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infoexpert21

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