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NCERT Solutions Class 9 Mathematics Solutions for Heron’s Formula - Exercise 12.2 in Chapter 12 - Heron’s Formula
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A triangle and a parallelogram have the same base and the same area. If the sides of the
triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find
the height of the parallelogram
Answer:
Given,
It is given that the parallelogram and triangle have equal areas.
The sides of the triangle are given as 26 cm, 28 cm and 30 cm.
So, the perimeter = 26 + 28 + 30 = 84 cm
And its semi perimeter = 84/2 cm = 42 cm
Now, by using Heron's formula, the area of the triangle =
√[s (s-a) (s-b) (s-c)]
\begin{array}{l} =v[42(42-26)(46-28)(46-30)] \mathrm{cm}^{2} \\ =\sqrt{[46 \times 16 \times 14 \times 16] \mathrm{cm}^{2}} \end{array}
Video transcript
"hello students welcome to leader q a
video session
i am sef your math tutor and question
for today is
a triangle and a parallelogram have the
same base and same area
if the sides of the triangle are 26
centimeter
28 centimeter and 30 centimeter
and the parallelogram stands on the base
of 28 centimeter
find the height of the parallelogram now
it is given that
the parallelogram and the triangle have
equal areas
the sides of the triangle are given as
26 centimeter
and 28 centimeter
and 30
centimeter so the perimeter will be
equal to
26 plus 28 plus 30.
we have indicated parameter as p
and hence that is 84
centimeter the semi perimeter can be
found now
to find semi perimeter we have to add
all the side
and divide it by two so
semi perimeter of triangle
as that is equal to 26 plus 28
plus 30 upon 2
so s will be equal to 42 centimeter
now you can find the area to find the
area we have to use the harold's formula
so by using heron's formula
the area of the triangle can be given by
let it indicate as a
root of
s s minus a s minus
b and s minus c
a b c are the sides so as is
you have found that is
42 centimeter
so 42 42 minus 26
42 minus 28
and 42 minus 30
that will be equal to root of
46 into 16 into 14 into 16
and that will be centimeter square
because it is area and that will give
you
area will be equal to 336
centimeter square now let the height of
parallelogram be h
as the area of parallelogram is given
will be equal to area of triangle
we can compare both and find height
so we will continue over here
it is given that area of
parallelogram
will be equal to area of triangle
and hence 28 into h
that is base into height that is the
area of parallelogram
is equal to area we have found to be of
triangle that is 336
so height will be equal to 336 divided
by 28.
height of the parallelogram will be 12
centimeter
and that is our final answer so
if you have any query you can drop it in
our comment section and subscribe to
lido for more such q and a thank you for
watching
"
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