Question

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

Answer 1

$\huge\sf\pink{Answer}$

☞ Height of the triangle = 5.6 cm

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$\huge\sf\blue{Given}$

Area of parallelogram = Area of triangle

✭ Base × Height = Area of triangle

✭ 15cm × Height = Area of triangle

✭ Height = $\dfrac{1}{15} \times\sf{Area\:of\:triangle}$

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$\huge\sf\gray{To \:Find}$

➢ Height of the parallelogram?

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$\huge\sf\purple{Steps}$

We know that,

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

❍ Here, s represents semi-perimeter, and a, b, c are the sides of the triangle.

◕ a = 15 cm

◕ b = 14 cm

◕ c = 13 cm

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

$\leadsto\sf{s}=\dfrac{15+14+13}{2}$

$\leadsto\sf{s}=\dfrac{42}{2}$

$\leadsto \sf\green{{s}=21}$

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

➳ Area=$\sf \sqrt{21(21-15)(21-14)(21-13)}$

➳ Area =$\sf \sqrt{21\times6\times7\times8}$

➳ Area = $\sf \sqrt{7056}$

➳ Area = $\sf\green{84 cm{}^{2}}$

Now,

$\sf\dashrightarrow Height = \dfrac{1}{15} \times\sf{Area\:of\:triangle}$

$\sf\dashrightarrow Height = \dfrac{1}{15}\times84$

$\sf\dashrightarrow\orange{5.6\: cm}$

$\rule{170}3$

Answer 2

Answer:

Step-by-step explanation:

Given :-

Sides of triangle = 15 cm, 14 cm and 13 cm

Base of parallelogram = 15 cm

To Find :-

Height of parallelogram

Formula to be used :-

Area of triangle = √s(s - a) (s - b) (s - c)

Area of parallelogram = Base × height

Solution :-

Semi perimeter = 15 + 14 + 13/2 = 42/2 = 21

Now, Area of triangle = √s(s - a) (s - b) (s - c)

⇒ Area of triangle = √21(21 - 15) (21 - 14) (21 - 13)

⇒ Area of triangle = √21(6) (7) (8)

⇒ Area of triangle = 3 × 7 × 3 × 2 × 7 × 2 × 2 × 2

⇒ Area of triangle = 3 × 7 × 2 × 2

⇒ Area of triangle = 84 cm²

Now,

Let h be the height of the parallelogram,

Area of parallelogram = Base × height

⇒ Area of parallelogram = 15 × h

⇒ Area of parallelogram = 15h cm²

Its given that

Area of triangle = Area of parallelogram

⇒ 84 = 15 h

⇒ 84/15 = h

⇒ h = 5.6 cm

Hence, the height of the parallelogram is 5.6 cm.