Question

The sides of a triangle are in the ratio 3:4:5.If its perimeter is 60cm .Find its area * pls answer feast.

Answer 1

Step-by-step explanation:

3x+4x+5x=60

12x=60

x=5

3x=15 cm

4x=20 cm

5x=25 cm

15^2+20^2=25^2

Triangle is right angled.

Area

=base×height÷2

=20×15÷2

=150cm^2

Hope it helps...

Answer 2

Let the ratio be x.

Then, sides of given triangle will be:

• First side = 3x
• Second side = 4x
• Third side = 5x

Given perimeter = 60cm.

Now,

$\tt perimeter \: of \: triangle = sum \: of \: all \: sides \\ \tt \implies 60cm = 3x + 4x + 5x \\ \tt \implies 60cm = 12x \\ \tt \implies x = \dfrac{60}{12}$

$\large \implies {\boxed {\tt \green {x = 5 }}}$

∵ Sides of triangle will be,

• First side = 3x = 3 × 5 = 15
• Second side = 4x = 4 × 5 = 20
• Third side = 5x = 5 × 5 = 25

_________________________

Answer

Let assume,

➣1st side = a

➣ 2nd side = b

➣ 3rd side = c

☛ By using Heron's Formula,

$\tt \implies s = \dfrac{1st \: side +2nd \: side + 3rd \: side}{2} \\ \\ \tt \implies s = \frac{15 + 20 + 25}{2} \\ \\ \tt \implies \: s = \frac{60}{2} \\ \\ \: \tt \implies s = 30$

Now,

✏ Area of triangle will be,

$= \tt \implies \sqrt{s(s - a)(s - b)(s - c) } \\ \\ \tt \implies = \sqrt{30(30 - 15)(30 - 20)(30 - 25)} \\ \\ \tt \implies = \sqrt{30(15)(10)(5)} \\ \\ \tt \implies = \sqrt{30 \times 750} \\ \\ \tt \implies = \sqrt{22500}$

$\large \implies \boxed {\boxed {\tt \blue { = 150cm{}^{2}}}}$

Hence,

☛ Area of triangle is 150 cm².