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kolbaska11 [484]
3 years ago
7

The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find t

he length of the segment determined by the points of intersection between the line and the other two sides of the triangle. WHOEVER SEES THIS PLEASE HELP ME ASAP!

Mathematics
1 answer:
sp2606 [1]3 years ago
8 0

Answer:

Length of DE is : 18√2 units

Step-by-step explanation:

The length of a side of a triangle is 36.

To calculate : The length of the segment DE

Now, the two parts of triangle have equal area ∴ Area(ADE) = Area(BDEC)

\implies Area(ADE)=\frac{1}{2}\times Area(ABC) \\\\\implies \frac{Ar(ADE)}{Ar(ABC)}=\frac{1}{2}

In ΔABE and ΔABC,

∠A = ∠A     (Common angles)

∠ABE = ∠ABC   (Corresponding angles are always equal)

By AA postulate of similarity of triangles, ΔABE ~ ΔABC.

Hence by area side proportionality theorem

\frac{Ar(ADE)}{Ar(ABC)}=(\frac{DE}{BC})^2\\\\\implies \frac{1}{2}=\frac{DE^2}{36^2}\\\\\implies DE^2=\frac{36^2}{2}\\\\\bf\implies DE=18\sqrt{2}\textbf{ units}

Hence, length of DE is 18√2 units

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