Question

Side of the triangle are in the ratio of 5 : 7 : 9 and its perimeter is 42 cm find its side and area

Answer 1

Answer:

The sides are 10cm, 14cm and 18cm.

The area of the triangle is 21√11cm²

Step-by-step explanation:

Let the sides of triangle be 5x, 7x and 9x

(taken these values frm the ratios given)

Given,

Perimeter=42cm

Perimeter=s+s+s

42=5x+7x+9x

42=21x

42/21=x

2=x

Now, substituting the values

5x=5×2=10cm

7x=7×2=14cm

9x=9×2=18cm

Therefore, the values of sides of the triangle are 10cm, 14cm and 18cm respectively.

Area=√s(s-a)(s-b)(s-c)

First, we will find s

s=a+b+c/2

=10+14+18/2

=42/2

=21

So,

s=21

a=10

b=14

c=18

Now, substituting the values in herons formula

=√s(s-a)(s-b)(s-c)

=√21(21-10)(21-14)(21-18)

=√21(11)(7)(3)

=√4851

=√3×3×7×7×11

=3×7√11

=21√11

Hence, the area is 21√11 cm²

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Answer 2

The sides are 10 cm, 14 cm, and 18 cm. The area of the triangle is $21\sqrt11$ $cm^2$

Step-by-step explanation:

Let the sides be a = 5y, b = 7y, and c = 9y

The perimeter = sum of all sides,

Thus, Perimeter = a + b + c = $5y + 7y + 9y = 42$

Adding, we obtain, $21y =42$

or, $y =\frac{42}{21}$ $=2$

Thus, the lengths of the sides are:

a = $5y = 5\times 2 = 10$

b = $7y = 7\times 2 = 14$

c = $9y = 9\times 2 = 18$

Thus, the three sides are a = 10 cm, b = 14 cm, and c = 18 cm.

To find area, we can use Heron's Formula:

Finding semi-perimeter (s)

$s =\frac {a+b+c}{2}$ = $\frac{10+14+18}{2}$ = $\frac{42}{2}$ = 21 cm

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

= $\sqrt 21(21-10)(21-14)(21-18)$

= $\sqrt 21(11)(7)(3)$

= $\sqrt (3)(7)(11)(7)(3)$

= $21\sqrt 11$ $cm^2$