Question

the length of the of triangle are the ratio 3:4:5 and its perimeter is 144cm. find its area by using Herons formula​

Answer 1

Solution :

In a given triangle , its sides are in the ratio of 3 : 4 :5 .

Let us assume that these sides are 3x, 4x and 5x respectively.

Perimeter :

> 3x + 4x + 5x

> 12 x

But, the perimeter is given as 144 cm .

So

12 x = 144

> x = 12

Side 1 = 3x = 3 * 12 = 36 cm

Side 2 = 4x = 4 * 12 = 48 cm

Side 3 = 5x = 5 * 12 = 60 cm

Using Herons Formula :

Semi perimeter , S = 144/2 = 72 cm .

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

> Square root of [ 72 * 36 * 24 * 12 ]

> 12 * 12 * Square root of [  4* 3 * 2 ]

> 12 * 12 * 2 root 6

> 288 root 6 m^2 .

This is the required answer.

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Answer 2

Step-by-step explanation:

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$\bf{\bigstar}$ $\text{\large\underline{\bf{Question:-}}}$

:$\Longrightarrow$ The length of the of triangle are the ratio 3:4:5 and its perimeter is 144cm. find its area by using Herons formula ?

$\bf{\bigstar}$ $\text{\large\underline{\bf{To\ Find:-}}}$

:$\Longrightarrow$ ● We have to find the area of triangle by using Herons formula.

$\bf{\bigstar}$ $\text{\large\underline{\bf{Given:-}}}$

:$\Longrightarrow$ ● The length of the triangle are in the ratio = 3 : 4 : 5.

:$\Longrightarrow$ ● The perimeter of the triangle = 144cm.

$\bf{\bigstar}$ $\text{\large\underline{\bf{Solution:-}}}$

:$\Longrightarrow$ Let the sides of triangles are 3x,4x and 5x.

:$\Longrightarrow$ And perimeter of the triangle is 144cm.

:$\Longrightarrow$ So, 3x + 4x + 5x = 144

:$\Longrightarrow$ 12x = 144

:$\Longrightarrow$ $\mathrm{x\ =\ \dfrac{144}{12}}$

:$\Longrightarrow$ x = 12.

$\bf{\bigstar}$ $\text{\large\underline{\bf{So,\ the\ sides\ of\ the\ triangle:-}}}$

:$\Longrightarrow$ 3x = 3 × 12 = 36cm.

:$\Longrightarrow$ 4x = 4 × 12 = 48cm.

:$\Longrightarrow$ 5x = 5 × 12 = 60cm.

:$\Longrightarrow$ So, the longest sides is 60cm.

$\bf{\bigstar}$ $\text{\large\underline{\bf{According\ to\ the\ question:-}}}$

:$\Longrightarrow$ Area of triangle = $\mathrm{\sqrt{s(s-a)(s-b)(s-c)}}$

:$\Longrightarrow$ Here, s = 72 and a = 36, b = 48, c = 60.

:$\Longrightarrow$ = $\mathrm{\sqrt{72(72-36)(72-48)(72-60)}}$

:$\Longrightarrow$ = $\mathrm{\sqrt{72(36)(24)(12)}}$

:$\Longrightarrow$ = $\mathrm{\sqrt{746496}}$

:$\Longrightarrow$ = $\fbox{864cm².}$ $\red{\bigstar}$

$\therefore$ $\fbox\purple{So,\ the\ area\ of\ triangle\ is\ 864cm².}$

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