Question

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_ A triangle and a parallelogram have the same base and same area. If the sides of the triangle are 15 cm, 14 cm and 13 cm and the parallelogram stands on the base 15 cm, find the height of the parallelogram.With Diagram _

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Answer 1

Answer:

The height of the parallelogram is 5.3 cm.

Step-by-step explanation:

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Answer 2

ANSWER

Given ;

→ Area of Parallelogram = Area of Triangle

→ Base × Height = Area of Triangle

→ 15 × Height = Area of Triangle

$height = \frac{1}{15} \times area \: of \: triangle$

According to Heron's Formula,

⇒Area of Triangle = √s (s-a) (s-b) (s-c)

⇔Here, s is the semi perimeter and a,b,c are the sides of the triangle

⇔Here a = 15 cm b = 14 cm c = 13 cm

$s = \frac{a + b + c}{2} \\ \\ s = \frac{15 + 14 + 13}{2} \\ \\ s = \frac{42}{2} \\ \\ s = 21$

tt

$area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{21 \: (21 - 15)(21 - 14)(21 - 13)} \\ \\ = \sqrt{21 \: (6)(7)(8)} \\ \\ = \sqrt{(7 \times 3) \: (6)(7)(8)} \\ \\ = \sqrt{(7 \times 7)(6 \times 3)(4 \times 2)} \\ \\ = \sqrt{(7 \times 7)(6 \times 3 \times 2)(4)} \\ \\ = \sqrt{(7 \times 7)(6 \times 6)(4)} \\ \\ = \sqrt{( {7}^{2} ) ({6}^{2} )( {2}^{2} )} \\ \\ = 7 \times 6 \times 2 \: \: \: \: \:..removed \: from \: square \: root \\ \\ = 42 \times 2 \\ = 84 \: cm ^{2}$

Area of Triangle = 84 cm²

⇒Now, Height of parallelogram

⇒Height = 1/15 × Area of Triangle

⇒Height = 1/15 × 84

Height = 5.6 cm