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
Answers
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
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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
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.