Question

1. The perimeter of a triangle is 450 m and its
sides are in the ratio 12 : 5: 13. Find the
area of the triangle.
o the same.

Please solve this question from Area and Perimeter of Plane Figures ​

Answer 1

Answer :-

• The area of triangle is 17280m².

Step-by-step explanation:

To Find :-

• The area of triangle

Solution:

Given that,

• The perimeter of triangle = 480m.
• The sides of triangle = 12:5:13

Assumption:

Let us consider the sides of triangle as 12x, 5x and 13x.

As we know that,

$\underline{\boxed{ \textbf{ \textsf{ \purple{Perimeter \: of \: triangle = Sum \: of \: all \: sides}}}}}$

Therefore,

• 12x + 5x + 13x = 480m

$\longrightarrow \: \sf{12x + 5x + 13x = 480}$

$\longrightarrow \: \sf{17x + 13x = 480}$

$\longrightarrow \: \sf{20x = 480}$

$\longrightarrow \: \sf{x = \dfrac{480}{20}}$

$\longrightarrow \: \sf{x = \cancel{\dfrac{480}{20}}}$

$\longrightarrow \: \sf{x = \dfrac{48}{2}}$

$\longrightarrow \: \sf{x = \cancel{ \dfrac{48}{2}}}$

$\longrightarrow \: \sf{x = 24}$

The sides are of ∆ are :-

• 12x = 12*24 = 288m
• 5x = 5*24 = 120m
• 13x = 13*24 = 312m.

Now, Semi-perimeter of triangle :-

We know that,

$\bigstar \: \underline{ \boxed{ \sf{Semi-perimeter \: of \: \triangle = \dfrac{Sum \: of \: all \: sides}{2}}}}$

Therefore,

$\longrightarrow \: \sf{ \dfrac{288 + 120 + 312}{2}}$

$\longrightarrow \: \sf{ \dfrac{720}{2}}$

$\longrightarrow \: \sf{ \cancel{\dfrac{720}{2}}}$

$\longrightarrow \: \sf{360}$

Now, The area of ∆ :-

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

Where,

• a, b and c are the three sides of triangle.

$\sf{ \longrightarrow \: \sqrt{s(s-a)(s-b)(s-c)}}$

$\sf{ \longrightarrow \: \sqrt{360(360 - 288)(360 - 120)(360 - 312)}}$

$\sf{ \longrightarrow \: \sqrt{360(72)(240)(48)}}$

$\sf{ \longrightarrow \: \sqrt{360 \times 72 \times 240 \times 48}}$

$\sf{ \longrightarrow \: \sqrt{298598400}}$

$\sf{ \longrightarrow \: \boxed{ \sf{ \red{17280}}}}$

Hence, The area of triangle is 17280m².