Question

Find the area of a triangle who's perimeter is 180cm and two of its sides are 80cm and 18cm. Also calculate the altitude of triangle corresponding to the shortest sides

Answer 1

Let the third side be x

Perimeter of triangle=Sum of its sides

180=80+18+x

180-98=x

x=82 cm

Let a=80cm b=18cm and c=82cm

s=a+b+c/2

=80+18+82/2

=180/2

=90cm

From heron's formula

Area of triangle=√s(s-a)(s-b)(s-c)

=√90(90-80)(90-18)(90-82)

=√90*10*72*8

=√9*10*10*9*8*8

=9*10*8

=720cm2

Area of trangle=1/2 x b x h

720=1/2*18*h (since the shortest side is 0f 18cm)

720=9h

720/9=h

80cm=h

Answer 2

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

__________________________

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

Sides,

a = 80

b = 18

perimeter (p) = 180

$\bold{\huge{\underline{\underline{\rm{ To\:Find :}}}}}$

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

__________________________

The herons formula to find Area of Triangle is :

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

Where s is half perimeter.

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

__________________________

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

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 -

$a = \frac{1}{2} \times width (b) \times height (h)$

So,

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

$720 = 9 \times (h)$

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

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

__________________________

───── ❝ TheEnforceR ❞ ─────

Mark as Brainliest !! ✨✨