Question

a triangle and a parallelogram have the same base and same area if the sides of triangle are 26 CM 28 cm and 30 cm and a parallelogram stand on the base 28 cm find the height of the parallelogram.... yrrrrre btadooo koi brainliest krdugi ussko plzzzzzzzzZzzz

Answer 1

$\sf{\boxed{\bold{\tiny{Heya\: mate. Solution \: below}}}}$
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★ $<b><u><font color = "red">A͞͞n͞͞s͞͞w͞͞e͞͞r͞͞ ↓</font color></u></b>$





♠ Gívєn thαt thє tríαnglє ( ∆ ) αnd thє pαrαlєllσgrαm ( ||gm ) hαvє thє ѕαmє αrєα. ѕσ fírѕt wє wíll fínd thє αrєα σf tríαnglє uѕíng thє Hєrσn'ѕ fσrmulα.



♠ Given sides,

Side 1, a = 26 cm

Side 2, b = 28 cm

Side 3, c = 30 cm




So, semi perimeter (s)

$\sf{= \frac{a + b + c}{2}}$

$\sf{= \frac{26 + 28 + 30}{2}}$

$\sf{= \frac{84}{2}}$

$\sf{= 42}$




Then, area,

$\sf{=\sqrt{s(s-a)(s-b)(s-c)}}$

$\sf{=\sqrt{42(42-26)(42-28)(42-30)}}$

$\sf{=\sqrt{42\times 16 \times 14 \times 12}}$

$\sf{=\sqrt{1,12,896}}$

$\sf{= 336 {cm}^{2}}$




♠ Also, area of a parallelogram,

$\sf{= base \times height}$

$\sf{= 28 \times h(for height)}$

$\sf{= 28h}$





♠ But, A/Q, area of parallelogram = area of triangle.

$\sf{=> 336 = 28h}$

$\sf{=> h = \frac{336}{28}}$

$\sf{=> h = 12 cm}$



♥ •°• t̲̅h̲̅e̲̅ h̲̅e̲̅i̲̅g̲̅h̲̅t̲̅ o̲̅f̲̅ t̲̅h̲̅e̲̅ p̲̅a̲̅r̲̅a̲̅e̲̅l̲̅o̲̅g̲̅r̲̅a̲̅m̲̅ i̲̅s̲̅ 12 c̲̅m̲̅. ♥

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