Question

the perimeters of two similar triangles are 24 CM and 18 CM respectively. If one side of first triangle is 8cm, then what is the corresponding side of second triangle? ​

Answer 1

Given that,

Perimeter of first triangle = 24 cm

Perimeter of second triangle = 18 cm

One side of first triangle = 8 cm

Let ABC and PQR be two triangles

According to both triangle,

$\bigtriangleup ABC \sim \bigtriangleup PQR$

$\dfrac{AB}{PQ}=\dfrac{BC}{QR}=\dfrac{AC}{PR}=K$

$AB=k(PQ)$...(I)

$BC=k(QR)$....(II)

$AC=k(PR)$.....(III)

From equation (I), (II) and (III)

$AB+BC+AC=K(PQ+QR+PR)$

$K=\dfrac{AB+BC+AC}{PQ+QR+PR}$

Here, AB+BC+AC = perimeter of first triangle

PQ+QR+PR= perimeter of second triangle

We need to calculate the corresponding side of second triangle

Using equation (I)

$\dfrac{AB}{PQ}=K$

Put the value in the equation (I)

$\dfrac{8}{PQ}=\dfrac{21}{18}$

$PQ=\dfrac{8\times18}{21}$

$PQ=6\ cm$

Hence, The corresponding side of second triangle is 6 cm.