Question

If the sides of a triangle are in the ratio 3 : 4 :5 and its perimeter is 96m then find the area of the triangle if the answer is 384m

Answer 1

Let the sides are,

3x, 4x, 5x

, _____________

Perimeter = sum of all sides

96 = 3x+4x+5x

96= 2x

96/12 = x

8 = x

Now,

Checking whether the triangle is right angled triangle or not,

So,
(highest)² = (sum of square of small sides)

(5x)² should equal to (3x²) +(4x)²

25x² should equal to 9x² +16x²

25x² = 25x²

Hence, this is a right angled triangle,




Area = (base×height)/2


Area = (3x×4x)/2


Area = (3×8×4×8)/2

Area = 3×8×4×4


Area = 24×16

Area = 384 m²


I hope this will help you



-by ABHAY

Answer 2

Hi...☺

Here is your answer...✌

GIVEN THAT,

Sides of triangle are in the ratio 3:4:5

Let the common multiple be x

Then sides are 3x , 4x , 5x

Now,

Perimeter = 96 m [ Given ]

Sum of all sides = 96 m

3x + 4x + 5x = 96 m

12x = 96 m

x = 8 m

=> 3x = 3×8 = 24 m
=> 4x = 4×8 = 32 m
=> 5x = 5×8 = 40 m

Therefore ,

Sides of triangle are 24m,32m and 40m

=> a = 24 m
=> b = 32 m
=> c = 40 m

Now

Semi perimeter,

s = perimeter/2

s = 96 / 2

s = 48 m

=> s - a = 48 - 24 = 24 m
=> s - b = 48 - 32 = 16 m
=> s - c = 48 - 40 = 8 m

Now,

By Heron's formula

Area of triangle

$= \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{48 \times 24 \times 16 \times 8} \\ \\ = \sqrt{2 \times 24 \times 24 \times 2 \times 8 \times 8} \\ \\ = 2 \times 24 \times 8 \\ \\ = 384 \: {m}^{2}$