Question

2. 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 1

Step-by-step explanation:

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$\bf\underline{\underline{\red{Given:-}}}$

• A triangle and a parallelogram have the same base and the same area .

• The sides of the triangle are 26cm , 28cm and 30cm.

• The base of the parallelogram is 28cm.

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The height of the parallelogram.

$\bf\underline{\underline{\green{Solution:-}}}$

The sides of the triangle are 26cm, 28cm and 30cm

Now:-

$\sf s = \dfrac{a + b + c}{2}$

Here:-

• a = 26cm

• b = 28cm

• c = 30cm

$\sf s = \dfrac{ 26 + 28 + 30}{2}$

$\sf s = \dfrac{84}{2}$

$\sf s = 42$

$\sf Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

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

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

$\sf = 336$

$\sf \therefore \underline{\: \: \underline{ \: Area\: of \: triangle = 336m^{2}\: }\: \:}$

$\sf Since, \: Area \: of \: triangle = Area \: of \: parallelogram$

$\sf Area \: of \: parallelogram = 336cm^{2}$

$\sf Base \: of \: parallelogram = 28cm$

$\sf \leadsto Area \: of \: parallelogram = Base \times Height$

$\sf \implies 336 = 28 \times h$

$\sf \implies 336 = 28h$

$\sf \implies h = \dfrac{336}{28}$

$\sf \implies h = 12$

$\underline{\boxed{\purple{\rm \therefore Height \: of \: the \: parallelogram = 12cm}}}$