A. W. H. Davies in his poem 'Lesire', depicts the predicament of the modern man who has gained the whole world but lost his own soul. Why do people in cities normally face shortage of time! Bring out the contrast between the nature and * city life.
Answers
DEF are respectively the midpoints of sides AB, BC and CA of triangle ABC, then: Ratio of area of triangle DEF : area of triangle ABC = 1 : 4
Solution:
In the given question, we know Triangle DEF formed with midpoints is similar to the Outer Triangle ABC
On the basis of the similarity, we can say,
If two triangles are similar then the ratio of their area is equal to the square of the ratio of their corresponding sides
Mathematically can be written as :-
\frac{\text {area of triangle } D E F}{\text {area of triangle ABC}}=\left(\frac{D E}{A C}\right)^{2}
area of triangle ABC
area of triangle DEF
=(
AC
DE
)
2
Since, DECF is a parallelogram. So DE = FC
On substituting:
\frac{\text {area of triangle } D E F}{\text {area of triangle ABC}}=\left(\frac{F C}{A C}\right)^{2}
area of triangle ABC
area of triangle DEF
=(
AC
FC
)
2
Also, F is the midpoint of AC
\text { So } \mathrm{AC}=2 \times \mathrm{FC} So AC=2×FC
\begin{gathered}\begin{array}{l}{\frac{\text {area of triangle } D E F}{\text {area of triangle } A B C}=\left(\frac{F C}{2 F C}\right)^{2}} \\\\ {\frac{\text {area of triangle } D E F}{\text {area of triangle } A B C}=\frac{1}{4}}\end{array}\end{gathered}
area of triangle ABC
area of triangle DEF
=(
2FC
FC
)
2
area of triangle ABC
area of triangle DEF
=
4
1
Hence ratio of area of triangle DEF and triangle ABC is given as:
Ratio of area of triangle DEF : area of triangle ABC = 1 : 4
Learn more about midpoints of triangle
Find the vertices of a triangle, the midpoints of whose side are(3,1),(5,6,),(-3,2)
https://brainly.in/question/3073037
The mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to what?
https://brainly.in/question/5968686
. H. Davies in his poem 'Lesire', depicts the predicament of the modern man who has ... - did not match any documents.
Suggestions:
Make sure that all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords.