Question

If ΔABC ~ ΔPQR, the ratio of the area of ΔABC to the area of ΔPQR = 9 : 4 and AB = 12 cm, then the length of PQ is

Answer 1

Answer:

8cm

solution in the pic

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Answer 2

Step-by-step explanation:

Given: If ΔABC ~ ΔPQR, the ratio of the area of ΔABC to the area of ΔPQR = 9 : 4 and AB = 12 cm.

To find: The length of PQ is?

Solution:

We know that if two triangles are similar than ratio of their corresponding sides are equal.

Here,

ΔABC ~ ΔPQR

$\bf \frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$

and ratio of area of triangles is equal to ratio of squares of side.

$\bf \frac{Ar∆(ABC)}{Ar∆(PQR)}=\frac{AB^2}{PQ^2}$

Place the given ratios of area

$\frac{9}{4}=\frac{AB^2}{PQ^2}$

Take square root

$\frac{3}{2}=\frac{AB}{PQ}$

Put value of AB

$\frac{3}{2}=\frac{12}{PQ}$

$PQ=\frac{24}{3}$

$\bf PQ=8$cm

Final answer:

Length of PQ is 8 cm.

Hope it will help you.

Learn more:

1) In the given figure, length of AD is : (A) a √15 units (B) a² √15 units (c) a/2 V15 units (D) a/3 √15 units

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