Question

Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is

540cm. Find its area. ​

Answer 1

Step-by-step explanation:

plz mark me as brilliant

Answer 2

Question:

Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540cm. Find its area.

To find:

• Area of triangle

Given :

• Sides of a triangle are in the ratio= 12: 17: 25
• Perimeter of triangle = 540 cm

Let:

• Side 1 = 12x
• Side 2= 17 x
• Side 3 = 25x

Solution :

To find area of triangle first we should know length of sides of triangle

So first let's find sides of triangle

We know:

$\boxed{ \boxed{ \rm{}perimeter \: of \: triangle = Side_1 + Side_2 +Side_3 }}$

By using this formula we can find value of x

So let's find it!

$: \implies\sf{}perimeter \: of \: triangle = Side_1 + Side_2 +Side_3$

put value of Perimeter and sides which we have supposed.

$: \implies\sf{}540= 12x + 17x + 25x$

$: \implies\sf{}540= 54x$

$: \implies\sf{} \dfrac{540}{54} = x$

$: \implies\sf{} \cancel\dfrac{540}{54} = x$

$: \implies\underline{\boxed{\sf{}x = 10 \: cm}}$

Before finding values of sides of triangle let's Verify value of x

Verification:

$: \implies\sf{}540= 12x + 17x + 25x$

put value of x in this equation:

$: \implies\sf{}540= 12 \times 10+ 17 \times 10 + 25 \times 10$

$: \implies\sf{}540= 120+ 170 + 250$

$: \implies\underline{\boxed{\sf{}540= 540}}$

$\large \gray{ \rm\ddag\:Hence \: verified \: \ddag }$

Now Let's find length of sides of triangle:

Side 1:

• Side 1 = 12x
• Side 1 = 12×10
• Side 1 = 120 cm

Side 2:

• Side 2= 17x
• Side 2 = 17×10
• Side 2=170 cm

Side 3:

• Side 3= 25x
• Side 3= 25× 10
• Side 3= 250 cm

Now Let's find Area by using heroes formula:

So to find area first we should know value of semi perimeter:

We know:

$\boxed{\boxed{ \rm{}s = \dfrac{side_1 + side_2 + side_3}{2} }}$

by using this formula we can find value of semi perimeter

$: \implies\sf{}s = \dfrac{side_1 + side_2 + side_3}{2}$

insert values of side 1, side 2, side 3

$: \implies\sf{}s = \dfrac{120+ 170+ 250}{2}$

$: \implies\sf{}s = \dfrac{540}{2}$

$: \implies\sf{}s = \cancel\dfrac{540}{2}$

$: \implies\sf{}s = 270 \: cm$

Now Finally Let's find area:

We know:

$\boxed{\boxed{ \rm{}Area \: of \: triangle = \sqrt{s(s - side_1)(s - side_2)(s - side_3)} }}$

by using this formula we can find value of Area of triangle

$: \implies\sf{}Area \: of \: triangle = \sqrt{s(s - side_1)(s - side_2)(s - side_3)}$

put values of semi perimeter and sides of triangle:

$: \implies\sf{}Area \: of \: triangle = \sqrt{270(270- 120)(270 - 170)(270 - 250)}$

$: \implies\sf{}Area \: of \: triangle = \sqrt{270 \times 150 \times 100 \times 20}$

$: \implies\sf{}Area \: of \: triangle = \sqrt{27 \times 3 \times 10 {}^{6} }$

$: \implies\sf{}Area \: of \: triangle = {3}^{ \frac{4}{2} } \times {10}^{ \frac{6}{2} }$

$: \implies\sf{}Area \: of \: triangle = {3}^{2} \times {10}^{3}$

$: \implies\sf{}Area \: of \: triangle = 9\times 1000$

$: \implies \underline{ \boxed{\sf{}Area \: of \: triangle = 9000 \: {cm}^{2}}}$

______________________________________________