Question

the area of triangle is 60 cm square if the side of the triangle became four and then find the area of new triangle


i need full solution fast​

Answer 1

Answer:

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

_______________________

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

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

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

area=

s(s−a)(s−b)(s−c)

s=

2

perimeteroftriangle

_______________________

let,

a = 20cm

b = 15cm

c = 25cm

here,

\begin{gathered} \: \: \: \: \: \: \: \: \: \: { \tt s = \frac{60cm}{2} } \\ \\ \implies \boxed{ { \tt s = 30cm}}\end{gathered}

s=

2

60cm

⟹

s=30cm

then,area of triangle,A ;

\begin{gathered} { \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} }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}

A=

s(s−a)(s−b)(s−c)

⟹A=

30(30−20)(30−15)(30−25)

⟹A=

30×10×15×5

⟹A=

3×10×10×5×3×5

⟹A=10×3×5

⟹

A=150cm

2

therefore, area of triangle is 150 cm²

Answer 2

Answer:

60×2 =120

because if four sides are there it will be a square or rectangle in there are 2 triangle in these shapes and if area of 1 triangle is 60 so area of 2 triangle will be 129