Question

find area of triangle whose perimeter is180 sides are 80&18.calculate the altitudeof triangle corresponding to shortest sides

Answer 1

80 cm will be the answer

Answer 2

$\huge{\underline{\underline{\red{♡Solution→}}}}$

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$\bold{\huge{\underline{\underline{\rm{ Given :}}}}}$

Sides,

a = 80

b = 18

perimeter (p) = 180

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Altitude of Triangle or the height (h) of Triangle.

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The herons formula to find Area of Triangle is :

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

Where s is half perimeter.

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

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$\purple{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

P = 180

We know that

• P = a + b + c

So,

a + b + c = 180

80 + 18 + c = 180

c = 180 - 98

c = 82

$s = \frac{80+18+82}{2} \\ s = \frac{180}{2}$

$s = 90$

Now Area is ,

$a = \sqrt{90(90-80)(90-18)(90-82)} \\ a = \sqrt{90 \times 10 \times 72 \times 8}$

$a = \sqrt{518400}$

$\boxed{a =720 }$

Now We know that -

• $a = \frac{1}{2} \times </strong><strong>widt</strong><strong>h</strong><strong> (</strong><strong>b</strong><strong>)</strong><strong> \times </strong><strong>height</strong><strong> (</strong><strong>h</strong><strong>)</strong><strong>$

So,

$720 = \frac{1}{2} \times 18 \times (h)$

$720 = 9 \times (h)$

$h = \frac{720}{9}$

$\boxed{h = 80\:cm}$

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