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

6 cm (Option A)

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.

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

SOLUTION :-

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

⇒ ΔPQR is similar to ΔABC.

`=> (Area \: of \: PQR)/(Area \: of \: ABC ) = ((QR)/(BC))^2`

`=>(32)/(8) = ((QR)/(3))^2`

Root squaring both the sides ,

`=> \sqrt{((QR)/(3))^2} = \sqrt{(32)/(8) }`

`=> (QR)/(3) = √(4) =2`

Multiplying both the sides by 3 ,

`=> (QR)/(3) * 3 = 2 * 3`

`=> QR = 6 \:cm`