Question

find the area of a triangle whose side are in the ratio 5 is to 12 is to 3 and its perimeter is 60 CM​

Answer 1

$\boxed{\bf{\red{Correct\: Question:-}}}$

Find the area of a triangle whose side are in the ratio 5 :12:13 and its perimeter is 60 CM

• If there was 3 in the place of 13 our The triangle is not formed

• because sum of two sides of triangle is always greater than the third side

$\huge\mathbb{SOLUTION:-}$

• The Sides of triangle in ratio .which is

• 5:12:13

• And the perimeter=60cm

• Now first find the side of triangle

$\boxed{\sf{Perimeter\:of\: triangle=sum\:of\:all\:sides}}$

$\bf\underline{\red{According\:To\: Question:-}}$

• Let the side be x

• so Sides =5x , 12x and 13x

Perimeter=Sum of all sides

5x+12x+13x=60

30x=60

$\sf x= \cancel{\frac{60}{30}}=2$

• The value of x is 2

• so sides of triangle

• Is = 2× 5=10cm

• 2×12=24cm

• 2×13=26cm

We have to find the area of triangle

By heron's formula

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

where s is the semi perimeter

$\sf s=\frac{( a+b+c)}{2}$

$\sf\leadsto s=\frac{10+26+24}{2}\\ \\ \sf\leadsto s=\cancel{\frac{60}{2}}=30$

semi perimeter=30

Now the area of ∆

$\sf\implies Area=\sqrt{30(30-10)(30-26)(30-24)}\\ \\ \sf\implies Area=\sqrt{30\times 20\times 4\times 6}\\ \\ \sf\implies Area=\sqrt{10\times 3\times 10\times 2\times 4\times 3\times 2}\\ \\ \sf\implies Area=10\times 3\times 2\times 2\\ \\ \sf\implies Area=120cm{}^{2}$

$\boxed{\sf{\purple{Area\:of\: triangle=120cm{}^{2}}}}$