Question

a triangle and the parallelogram have same base and same area ... if tge sides are 26 28 and 30 cm . base of parallelogram 28 cm . find the height . plz do full solution ..... urgently plzz

Answer 1

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In Δ

a = 26cm

b = 28

c = 30cm

$s = \frac{a + b + c}{2} \\ \\ = > \frac{26 + 28 + 30}{2} = \frac{84}{2} = 42cm$

Area of the triangle,

$= \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{42(42 - 26)(42 - 28)(42 - 30)} \\ \\ = \sqrt{42(16)(14)(12)} \\ \\ = \sqrt{(6 \times 7)(16)(7 \times 2)(6 \times 2)} \\ \\ = > 6 \times 4 \times 7 \times 2 = 336c {m}^{2}$

Let the height of the parallelogram be h cm.

Then, area of the parallelogram,

Base × Height = 28 × h

According to the question,

$28h = 336 \\ \\ = h = \frac{336}{28} \\ \\ = > h = 12cm$

Hence, the height of the parallelogram is 12cm

$\large{\boxed{\bold{Hope\:it\:helps\:you!}}}$

Answer 2

Base of triangle=Base of parallelogram
Area of triangle =Base of parallelogram
a=26cm,b=28cm, c= 30cm
perimeter = 26+28+30=84cm
S(semiperimeter)=1/2× perimeter
=1/2×84=42
Using Heron's formula
Area of triangle =Root s×s-a×s-b×s-c
Root 42(42-26)(42-28)(42-30)
=336cm2(2 means square)
Area of triangle = Area of parallelogram
336= base× height
height = 336/base
height = 12cm