Question

in triangle abc angle b=90 degree and d is the point of ac. if ab=20 cm and bd =14.5 cm,find the area and the perimeter of triangle abc

Answer 1

Here we form a rectangle ABCE , Here AB = CE , AB | | CE and BC = EA , BC | | EA

And we know in rectangle diagonals are equal in length and bisect each other , So

Here AC and BE are diagonals of rectangle ABCE and they intersect at " D " , So

BD = AD = DC = DE = 14.5 cm ( As given BD = 14.5 cm )

Then ,

AC = AD + DC = 14.5 + 14.5 = 29 cm

Now we apply Pythagoras theorem in triangle ABC and get

AC2 = AB2 + BC2

292 = 202 + BC2

841 = 400 + BC2

BC2 = 441

BC = 21 cm

We know Area of triangle = 12× Base× Height ,

In triangle ABC , Base = BC = 21 cm and Height = AB = 20 cm

So,

Area of triangle ABC = 12× 21 × 20

= 21 × 10 = 210 cm2 ( Ans )

AndWe know perimeter of triangle = Sum of all sides , So

Perimeter of triangle ABC

=> 20 + 21 + 29 = 70 cm ( Ans )

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@GauravSaxena01