Math, asked by davinderchahal, 6 months ago

the following figure shows a right angle triangle ABC with angle B = 90 degree AB=15cm and AC= 25cm D is the midpoint of BC and CD=7cm. if DE perpendicular to AC find the length of DE​

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Answers

Answered by pradnya250604
41

Answer:

IN ΔABC

AB²+BC²=AC² . (PYTHAGORAS THM)

15²+BC²=25²

BC²=625=400

BC=√400=20 CM

NOW, BC=BD+CD

          BD=20-7=13 CM

ALSO,

ar(ΔABC)=ar(ΔACD) + ar(ΔABD)

1/2 *20*15= (1/2 *DE*25) + (1/2 *13*15)

20*15=25DE + 13*15

300-195=25DE

105=25DE

4.2 CM=DE

STAN KPOP IDOLS

Answered by Anonymous
3

Given:

AB=15 cm

AC=25 cm

CD=7 cm

To find:

The length of DE

Solution:

The length of DE is 4.2 cm.

We can find the length by following the given steps-

We know that the line AD divides CD into two equal parts.

So, CD=DB=7cm

Since AD divides BC equally, AD is the median of the triangle ABC.

We know that the median of a triangle divides it into two equal parts.

The median AD divides the ΔABC into ΔABD and ΔADC.

The area of ΔABD and ΔADC is equal. (A median divides a triangle into two triangles whose area is equal)

So, we will equate the areas of both the triangles to find the length of DE.

We know that the area of a triangle=1/2×base×height

In ΔABD, the base is BD and the height is AB.

So, the area of ΔABD=1/2×BD×AB

=1/2×7×15

=52.5 cm^{2}

Similarly, in ΔADC, AC is the base and DE is the height.

The area of ΔADC=1/2×AC×DE

=1/2×25×DE

=12.5 DE

Now, the area of ΔADC=area of ΔABD.

52.5=12.5×DE

DE=52.5/12.5

DE=4.2 cm

Therefore, the length of DE is 4.2 cm.

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