Question

the ratio of the areas of the two similar triangles are 9:16 one of the One triangle is 3 centimetres find the other length of the corresponding side​

Answer 1

Answer:

The length of the corresponding side is 4 cm.

Step-by-step explanation:

Given

Ratio of the areas of two similar triangles = 9 : 16 = 9/16

Length of one of the side of a similar triangle = 3 cm

Let the length of the corresponding side be x cm

We know that

Ratio of areas of two similar triangles = Ratio of the squares of their corresponding sides

⇒ 9/16 = (3)²/(x)²

⇒ 9/16 = 9/x²

⇒ 16/9 = x²/9

⇒ (16/9) * 9 = x²

⇒ 16 = x²

⇒ √16 = x

⇒ 4 = x

⇒ x = 4 cm

Therefore the length of the corresponding side is 4 cm.

Answer 2

》 The ratio of two similar triangles are 9:16and one of the triangle is 3 cm.

We know that..

Ratio of two similar triangle is equal to the ratio of square of their ccorresponding sides.

Let ratio of two triangles be "a" and "b".

Here,

a = 9 and b = 16

And ratio of two sides be "c" and "d".

Here,

c = 3 and we have to find "d".

So,

$\dfrac{a}{b}\:=\:\dfrac{c}{d}$

According to question,

=> $\dfrac{a}{b}\:=\:\dfrac{ {c}^{2} }{ {d}^{2} }$

Put the known values

=> $\dfrac{9}{16}\:=\:\dfrac{ {(3)}^{2} }{ {d}^{2} }$ _____ (eq 1)

=> $\dfrac{9}{16}\:=\:\dfrac{ 9 }{ {d}^{2} }$

9 throughout cancel,

=> $\dfrac{1}{16}\:=\:\dfrac{ 1 }{ {d}^{2} }$

Cross multiply them

=> d² = 16

=> d = 4

Length of corresponding side is 4 cm.

☆ VERIFICATION :

Put value of "d" in (eq 1)

=> $\dfrac{9}{16}\:=\:\dfrac{ ({3)}^{2} }{ {(4)}^{2} }$

=> $\dfrac{9}{16}\:=\:\dfrac{ 9 }{ 16 }$