Question

the ratio of equal and unequal side of an isosceles triangle is 3 ratio 5 if its perimeter is 110 cm find its area​

Answer 1

Answer:

let the three sides be 3x,3x and 5x

Step-by-step explanation:

therefore;

3x+3x+5x=110

11x=110

x=10

Hence the sides are30,30 ,50 cm

Answer 2

The area of the triangle is $125\sqrt{11}cm^2$

Step-by-step explanation:

• Let the two equal sides of the isosceles triangle are $3x$ and the unequal side is $5x.$

• The perimeter of the triangle =  sum of lengths of all the sides

So$, 110 = 3x + 3x + 5x$

$110 = 11x$

$x = 10$

• Hence, the equal sides are $3x = 3\times 10 = 30 cm$ each, and the unequal side is $5x = 5\times 10 = 50 cm$

• To find the area, we can use Heron's formula  

Finding semi-perimeter$,s = 110/2 = 55$

$a = 30, b = 30, c= 50, and s= 55$

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

$=\sqrt{55(55-30)(55-30)(55-50)}$

$= \sqrt{55(25)(25)(5)}$

$= 125\sqrt{11}$ $cm^2$