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If the sides of A triangle and a parallelogram have the same base and the 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.


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Answer 1

Given :-

• Side of A triangle = 26 cm , 28cm and 30 cm
• Parallelogram stand on the base = 28 cm
• The base of triangle and parallelogram is equal.

To Find :-

• The height of parallelogram = ?

Solution :-

To calculate the height parallelogram , at first we have to find out the area of triangle then calculate the height of parallelogram.

Calculation for triangle ABC :-

• Side = 26 , 28 , 30
• a = 26 , b = 28. c = 30

⇒ S = a + b + c/2

⇒ S = 26 + 28 + 30/2

⇒ S = 84/2 ⇒S = 42

• Area of the triangle by herons formula :-

⇒ Area = √s(s - a) × (s - b) × (s - c)

⇒ Area = √42(42 - 26) × (42 - 28) × (42 - 30)

⇒ Area = √42 × 16 × 14 × 12

⇒ Area = √(7 × 6) × 16 × (7 × 2) × (6 × 2)

⇒ Area = 7 × 6 × 4 × 2

⇒ Area = 336cm²

• Now calculate the height of parallelogram as you can see in the given A triangle and parallelogram has same base or the triangle's base also stand on the base of parallelogram. So, it's area also will be equal.

⇒ Area of p||gram = Area of triangle

⇒ Base × height = 336

⇒ 28 × height = 336

⇒ height = 336/28

⇒ height = 12cm

Hence,

• The height of parallelogram = 12m

Verification :-

⇒ Area of parallelogram = Area of ∆

⇒ Base × height = 336

⇒ 28 × 12 = 336

⇒ 336 = 336 (Hence, verified)

Answer 2

⇝Given :-

• Sides of a triangle have same base.
• Sides of triangle = 26cm , 28cm , 30cm
• Base of parallelogram = 28cm

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⇝To Find :-

• Height of parallelogram = ?

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⇝Solution :-

❒ We know that :

${\large{\red{\bigstar \: \: \: \: \: \: {\orange{\underbrace{\underline{\green{\bf{Semi - Perimeter = \frac{a + b + c}{2} }}}}}}}}}$

${\large{\red{\bigstar \: \: \: \: \: \: {\orange{\underbrace{\underline{\green{\bf{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}}}}}}}$

❒ Area of triangle :

✏ Semi - Perimeter :

${\large{:{\longmapsto{\bf{Semi - Perimeter = \frac{a + b + c}{2} }}}} }$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{26 + 28 + 30}{2} }}}} }$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\cancel \frac{84}{2} }}}} }}$

${\large{\orange{\dashrightarrow{\blue{\underline{\bf{42 cm}}}}}}}$

✏ Area :

${\large{:{\longmapsto{\bf{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}} }$

${\large{:{\longmapsto{\bf{Area = \sqrt{42(42 - 26)(42 - 28)(42 - 30)} }}}} }$

${\large{:{\longmapsto{\bf{Area = \sqrt{42 \times 16 \times 14 \times 12} }}}} }$

${\large{\orange{\dashrightarrow{\blue{\underline{\bf{336 \: {cm}^{2} }}}}}}}$

❒ Height of parallelogram :

✏ Here :

• Base = 28 cm
• Area = area of triangle = 336 cm²(given)
• Height = ?

✏ Height :

${\large{:{\longmapsto{\bf{Area \: of \: parallelogram = Base \times Height}}}}}$

${\large{:{\longmapsto{\bf{336 = 28 \times height}}}}}$

${\large{:{\longmapsto{\bf{Height = {\cancel\frac{336}{28} }}}}}}$

${\large{\red{:{\twoheadrightarrow{\purple{\underline{\overline{\boxed{\bf{Height = 12 cm}}}}}}}}}}$

❒ Hence :

${\huge{\purple{\underline{\red{\underline{\pink{\pmb{\mathfrak{Height = 12cm}}}}}}}}}$

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