In ∆ABC, .D on AC and .E on AB if ∠ADE = ∠B, AD = 7.6 cm, AE = 7.2 cm, BE = 4.2 cm and BC = 8.4 cm, then find DE..
a) 5.6cm b) 6.6cm c) 7.6cm d) 7.2cm
Answers
Answer:
D is mid-point of side BC
E is mid-point of side CA
F is mid-point of side AB
AB = 6.2 cm
DF = 3.8 cm
The perimeter of ΔABC = 21 cm
To find:
(I) The length of DE
(II) The length of AC
(III) The length of FE
Solution:
We know,
\boxed{\bold{\underline{MID-POINT\:THEOREM}}}:
MID−POINTTHEOREM
: This theorem states that the line segment joining the two sides of a triangle at the midpoints of those two sides is half the length of the third side.
(I). Finding the length of DE:
In the given ΔABC,
D and E are the midpoints of the side BC and CA of the triangle and the third side opposite to DE is AB whose length is 6.2 cm.
Therefore, using the mid-point theorem, we get
DE = \frac{1}{2} \times AB = \frac{1}{2} \times 6.2 = 3.1 \:cmDE=
2
1
×AB=
2
1
×6.2=3.1cm
Thus, \boxed{\bold{DE = 3.1\: cm}}
DE=3.1cm
(II). Finding the length of AC:
In the given ΔABC,
D and F are the midpoints of the side BC and AB of the triangle and the third side opposite to DF, whose length is given as 3.8 cm, is AC.
Therefore, using the mid-point theorem, we get
AC = 2 \times DF = 2 \times 3.8 = 7.6 \:cmAC=2×DF=2×3.8=7.6cm
Thus, \boxed{\bold{AC = 7.6\: cm}}
AC=7.6cm
(III). Finding the length of FE:
We know,
The perimeter of a triangle = AB + BC + CA
Substituting the values of perimeter = 21 cm, AB = 6.2 cm & AC = 7.6 cm, we get
⇒ 6.2 + BC + 7.6 = 21
⇒ 13.8 + BC = 21
⇒ BC = 21 - 13.8
⇒ BC = 7.2 cm
In the given ΔABC,
F and E are the midpoints of the side AB and CA of the triangle and the third side opposite to FE is BC whose length is 7.2 cm.
Therefore, using the mid-point theorem, we get
FE = \frac{1}{2} \times BC = \frac{1}{2} \times 7.2 = 3.6 \:cmFE=
2
1
×BC=
2
1
×7.2=3.6cm
Thus, \boxed{\bold{FE = 3.6\: cm}}
FE=3.6cm
.
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Also View:
Prove mid-point theorem
https://brainly.in/question/2322835
triangle ABC, P, Q and R are the midpoints of AB, BC and CA respectively. AB= I2 cm, BC = 16 cm and CA = 20 cm, find the perimeter of trapezium PB
Answer:
a) 5.6 cm
Step-by-step explanation:
