Question

Triangle PQR with area 32cm square and base QR is an enlargement of Triangle ABC with area 8 cm square and base BC=3cm , what is the length of QR in cm?
a) 6
b) 8
c) 10
d) 12

Answer 1

I think the answer is A but i could be wrong

Answer 2

Answer:

6 cm (Option A)

Step-by-step explanation:

GIVEN :-

• ΔPQR whose area is 32 cm² & has base QR.
• ΔABC whose area is 8 cm² & has base BC = 3 cm
• ΔPQR is an enlarged figure of ΔABC.

TO FIND :-

• Length of QR

FACTS TO KNOW BEFORE SOLVING :-

Lets say there are two triangles ΔABC & ΔXYZ , who are similar to each other.

$=> \frac{Area \: of \: ABC}{Area of XYZ} = (\frac{AB}{XY})^ {2} = (\frac{BC}{YZ})^2 = (\frac{AC}{XZ} )^2$

SOLUTION :-

In the question it's given that ΔPQR is an enlarged figure of ΔABC.

⇒ ΔPQR is similar to ΔABC.

$=> \frac{Area \: of \: PQR}{Area \: of \: ABC } = (\frac{QR}{BC})^2$

$=>\frac{32}{8} = (\frac{QR}{3})^2$

Root squaring both the sides ,

$=> \sqrt{(\frac{QR}{3})^2} = \sqrt{\frac{32}{8} }$

$=> \frac{QR}{3} = \sqrt{4} =2$

Multiplying both the sides by 3 ,

$=> \frac{QR}{3} \times 3 = 2 \times 3$

$=> QR = 6 \:cm$