Question

the perimeter of a triangle is 36 cm and the sides are in the ratio 2 : 5 : 5 ,then

find the area of the triangle .​

Answer 1

Answer:

Let sides are a, b and c, a = 3x, b = 4x, c = 5x

Perimeter = a + b + c

=> 36 = 3x + 4x + 5x

=> x = 3

a = 9 cm, b = 12 cm and c = 15 cm

Step-by-step explanation:

Area =√s(s-a)(s-b)(s-c)

= √18(18-9)(18-12)(18-15)

=√18×9×6×3

=54cm2

Answer 2

Solution

✒️Here the perimeter of the triangle is given as 36 cm and the ratio of sides is given as 2:5:5.

✒️So we have to find the area by Herons Formula . But in order to find the area of triangle we first need to find the sides of the triangle.

Now,

$\sf言\color{pink}{Let's \: us \: assume \: the \: ratio \: of \: the \: sides \: as \: 2x ,5x \: and 5x.}$

we know that,

${\underline {\boxed{ \sf {\color{grey}{perimeter \: of \: the \: triangle= sum \: of \: all \: sides }}}}}$

$so, \\ \sf{ \implies \: 2x+5x+5x = 36} \\ \\ \sf{ \implies12 x = 36} \\ \\ \sf{ \implies \: x= \frac{36}{12}} \\ \\ \sf{ \implies \color{blue}\: x= 3}$

so the value of x is 3

now subsitute the value of x in order to find the sides .

$\sf{ \to 2x = 2 ×3 = 6cm} \\ \sf{ \to5x = 5× 3= 15 cm}$

→ semi-perimetre = 36/2= 18 cm

$\sf{so \: the \: sides \: of \: triangle \: is \: 6cm, \: 15 cm \: and \: 15 cm}$

By herons formula the area of the triangle is

${ \underline{ \boxed{ \sf{area= \sqrt{ s(s-a)(s-b)(s-c)}}}}} \\ \\ \sf{ \implies \: area = √ 18×(18-6)(18-15)(18-15)} \\ \\ \sf{ \implies \: area = √ 18 × 12 × 3 ×3} \\ \\\sf{ \implies \: area = 18√6 cm²} \\ \\ \sf{\implies \: area = 18 × 2.44 } \\ \\ \sf{ \implies \: area = 43. 92cm²}$

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