Question

The perimeter of a triangle is 60 cm and the sides are in a ratio 4:3:5. Find its area.

Answer 1

Aɴsᴡᴇʀ

given :-

• perimeter of triangle = 60cm
• ratio of sides of triangle = 4:3:5

to find :-

• area of triangle ?

solution :-

we have, ratio of sides of a triangle is 4:3:5

let the sides of this triangle are 4x , 3x and 5x

and we know that,

perimeter of triangle = sum of sides of triangle

➪ 60 = 4x + 3x + 5x

➪ 60 = 12x

➪ 12x = 60

➪ x = 60/12

➪ x = 5

hence, x = 5 is the common multiple of sides of this triangle,

then sides of triangle are;

• 4 × 5 = 20cm
• 3 × 5 = 15cm
• 5 × 5 = 25cm

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now, find the area of triangle by heron's formula

if a,b and c are sides of a triangle then,

$\boxed{{ \bold{area= \sqrt{s(s - a)(s - b)(s - c)}} }} \\ \\ \boxed{ \bold{s = \frac{perimeter \: of \: triangle}{2} }} \: \: \: \:$

_______________________

let,

• a = 20cm
• b = 15cm
• c = 25cm

here,

$\: \: \: \: \: \: \: \: \: \: { \tt s = \frac{60cm}{2} } \\ \\ \implies \boxed{ { \tt s = 30cm}}$

then,area of triangle,A ;

${ \tt A = \sqrt{s(s - a)(s - b)(s - c)} } \: \: \: \: \: \\ \\ { \tt\implies A = \sqrt{30 (30 - 20)(30 - 15)(30 - 25)} } \\ \\ { \tt \implies A = \sqrt{30 \times 10 \times 15 \times 5} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt \implies \: A = \sqrt{3 \times 10 \times 10 \times 5 \times 3 \times 5} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt \implies A = 10 \times 3 \times 5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies\boxed{ \pink{\bold{A = 150 \: {cm}^{2} }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

therefore, area of triangle is 150 cm²