93.
What is common to capillary endothelium and
alveolar epithelium?
(1) Cuboidal epithelium specialised for absorption
(2) Squamous epithelium specialised for
absorption
(3) Squamous epithelium specialised for diffusion
(4) Cuboidal epithelium specialised for diffusion
Answers
Explanation:
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
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