Question

The area of a triangle is 108 cm2. If the respective ratio between height and base is 3:2, what is the perimeter of a square whose side is equal to twice the base of the triangle ?(in cm)

Answer 1

Question :-- The area of a triangle is 108 cm2. If the respective ratio between height and base is 3:2, what is the perimeter of a square whose side is equal to twice the base of the triangle ?(in cm)

Formula used :--

→ Area of ∆ = 1/2 * Base * Height .

→ Area of Square = 4 * side .

Solution :--

Let Base of ∆ = 2x .

Height of ∆ = 3x.

→ Area of ∆ = 1/2 * 2x * 3x = 3x².

Given, Area of ∆ = 108cm².

so, putting both Equal we get,

→ 3x² = 108

→ x² = 36

→ x = 6 .

So, Base of ∆ = 2x = 2*6 = 12cm. .

Now, it is given that , side of square is Twice base of ∆.

So,

→ side of Square = 2*12 = 24cm.

→ Perimeter of square = 4*24 = 96cm.

Hence, perimeter of Square whose side is Twice base of ∆ is 96cm..

Answer 2

Answer:

${\boxed{\bold\purple{Perimeter\:of\:square=96\:cm}}}$

Step-by-step explanation:

Given that:-

• $\bold\red{Area\:of\:triangle=108\:{cm}^{2}}$
• $\bold\green{Height:Base=3:2}$
• $\bold\red{Side=2\times Base}$
• $\bold\green{Perimeter\:of\:square=?}$

Let the base of triangle = 2x and the height of triangle = 3x .

${\boxed{\bold{Area=\frac{1}{2}\times Base \times Height}}}$

$\rightarrow\sf 108 = \frac{1}{2}\times 2x \times 3x \\\rightarrow\sf 108 =\frac{1}{2}\times {6x}^{2} \\\rightarrow\sf {6x}^{2} = 216 \\\rightarrow\sf {x}^{2} =\frac{216}{6} \\\rightarrow\sf {x}^{2} = 36 \\\rightarrow\sf x =\sqrt{36}\:cm \\\rightarrow\sf x = 6\: cm$

__________________________

Dimensions:-

Base of triangle = 2x =(2 × 6) = 12 cm

Height of triangle =3x=(3 × 6) = 18 cm

Now,

$\sf Side \:of\:square = 2 \times Base \\\rightarrow\sf Side \:of\:square = (2 \times 12)\:cm \\\rightarrow\sf Side \:of\:square = 24 \: cm$

${\boxed{\bold{Perimeter\:of\:square=4\times Side}}}$

$\rightarrow\sf Perimeter = (4 \times 24)\:cm$

$\rightarrow{\tt\purple{\boxed{Perimeter = 96\:cm }}}$

$\therefore\bold{\underline{Perimeter\:of\:square=96\:cm}}$