Question

6. A triangular table whose sides are in a ratio
3:4:5 and perimeter is 36 m, then find the area
of the table.​

Answer 1

$\huge\bold\red{Solution}$

The area of triangle is 54 cm².

$\huge\bold{Explanation}$

It is given that the sides of a triangle are in the ratio 3 : 4 : 5.

Let the length of sides are 3x, 4x and 5x.

It's perimeter is 36 cm.

$3x + 4x + 5x = 36$

$12x = 36$

$x = 3$

•The value of x is 3.

• The length of sides are 9, 12, 15.

•It is an right angled triangle because the sum of squares of two smaller sides is equal to the square of larger sides.

${9}^{2} + {12}^{2} = {15}^{2} = 225$

Here, the length of hypotenuse is 15 cm.

The area of triangle is

$\frac{1}{2} \times base \times height$

$\frac{1}{2} \times 9 \times 12 = 9 \times 6$

$= > 54 \: {cm}^{2}$