Question

Q22) The perimeter of a triangle is
300 metre if its sides are in the ratio
3:5:7 Find the area of the triangle.
(2 marks)​

Answer 1

Step-by-step explanation:

Ratio of sides = 3:5:7

Let sides be 3x, 5x, 7x

So 3x + 5x + 7x = 300m

15x = 300m

x = 20 m

Sides are 60m, 100m, 140m

s = 300/2=150

triangle=Ratio of sides = 3:5:7

Let sides be 3x, 5x, 7x

So 3x + 5x + 7x = 300m

15x = 300m

x = 20 m

Sides are 60m, 100m, 140m

s =300/2

=150

I.e area of triangle=√s(s-a)(s-b)(s-c)

√150(90)(50)(10)

5*3*10*3*3*10*5*10*10

100*5*3√3

1500√3m^3

Answer 2

GIVEN -

• perimeter of triangle
• ratio of sides = 3:5: 7

TO FIND -

• Area

SOLUTION

Let the ratio be 3x , 5x , 7x

Perimeter of triangle = Sum of three sides

300 = 3x + 5x + 7x

300 = 15x

300/15 = X

20 = X

sides of traingle =

3x = 3 × 20 = 60

5x = 5 × 20 = 100

7x = 7 × 20 = 140

S = 60 + 100 + 140 /2

= 300 /2

= 150

USING HERON'S FORMULA

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

= $\sf \sqrt{ 150(150-60)(150-100)(150-140)}$

= $\sf \sqrt{ 150(90)( 50)(10)}$

= $\sf \sqrt{ 150( 900)(50)}$

= $\sf \sqrt{ 150( 45000)}$

= $\sf \sqrt{ 3 \times 5 \times5 \times 2( 5 \times 3\times 3\times 1000)}$

= $\sf \sqrt{ 3 \times 3 \times 3 \times 5 \times 5 \times 2 \times 100}$

= $\sf \sqrt{ 3^2 \times 5^2 \times 6\times 100}$

= 3 × 5 $\sf \sqrt{ ( 3 \times 600)}$

= 15 $\sf \sqrt{ 1800 }$

= 15 $\sf \sqrt{ 3 \times 3 \times 2 \times 100 }$

= 15 × 3 $\sf \sqrt{ 2\times 2\times 5\times 5}$

= 45 [tex]\times 5\times 2[\tex]

= 45[tex]\times 10[\tex]

= 450

Area of triangle = 450 cm [ assume cm]