Question

The perimeter of a triangle is 54 cm and its sides are in the ratio 5:6:7. Find the area of the âle

Answer 1

Answer:

5+6+7/3= 54

6x =54

x=9 the area is 9

Answer 2

$\bf {\huge {\underline {\boxed{\sf\purple {Solution:-}}}}}$

Given,

Perimeter of the rectangle = 54 cm

Ratio of three sides = 5:6:7

Let common factor be x.

Now,

Three sides of the triangle will be 5x, 6x and 7x.

Also,

Perimeter of the triangle = sum of all three sides.

54 = 5x + 6x + 7x

54 = 18x

x = $\dfrac {54}{18}$

x = 3

➡ Pit the value of x in each side of the triangle

5x = 5 × 3 = 15 cm

6x = 6× 3 = 18 cm

7x = 7 × 3 = 21 cm

Now,

➡ To find area of Triangle

Side ( a ) = 15 cm; side ( b) = 18 cm: side ( c) = 21 cm

S = $\dfrac {a+b+c}{2}$

= $\dfrac {15+18+21}{2}$

= $\dfrac {54}{2}$

= 27 cm

Area of Triangle : $\sqrt {S (S -a)(S-b)(S-c)}$

= $\sqrt {27 ( 27-15) (27-18)(27-21)}$

= $\sqrt{27 (12)(9)(6)}$

= $\sqrt {3×3×3×2×2×3×3×3×3×2}$

= 3×2×3×3 $\sqrt {3×2}$

$\textbf {\underline {\underline {Answer :}}}$ 54 $\sqrt {6} { cm}^2$

_____________________________

$\huge\mathscr\orange {Be\:}\huge\mathscr\red {Brainly!!! }$