from a point in the interior of an equilateral triangle, perpendicular are drawn on the three sides. the lengths of the perpendicular are 8 cm,10 cm and 11 cm. find the area of the triangle carrect to two decimal places. take √3 = 1.73.
Answers
Answer:
Answer
Let x be the side of an equilateral triangle.
Therefore, its area =
4
3
x
2
Also, area ABC = ar(ΔADB)+ar(ΔBDC)+ar(ΔCDA)
=
2
1
×x×8+
2
1
×x×10+
2
1
×x×11
=
2
1
x×(8+10+11)=14.5x
Again, both areas are equal
∵
4
3
x
2
=14.5x
⇒x=
3
58
...[∵x
=0]
Therefore, area of the equilateral triangle =
4
3
x
2
=
4
3
×(
3
58
)
2
=
4
3
×
3
58×58
∼486cm
2
For an equilateral triangle of side a cm , the area is 12a×a×sin60∘=3√4a2 cm2 .
This triangle is divided into three triangles each with a base length of a and perpendicular heights of 8,10 and 11 cm respectively. So the total area is 12×a×8+12×a×10+12×a×11=14.5a cm2 .
So 3√4a2=14.5a
3√4a=14.5
a=583√ cm
Therefore, the area is 14.5×583√=485.55 cm2 .
Check: 3√4×(583√)2=485.55 cm.
Step-by-step explanation: