Question

Corresponding sides of two triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 $cm^{2}$, determine the area of the larger triangle.

Answer 1

Answer:

The area of the larger ∆ is 108 cm²

Step-by-step explanation:

Given:

Let the Smaller triangle be ΔABC & bigger triangle be ΔPQR and the corresponding sides be BC & QR  

ΔABC ~ ΔPQR.

Area of ΔABC = 48 cm².

BC : QR = 2 : 3  

ar(ΔABC)/ar( ΔPQR) = (BC/QR)²

[The ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.]

48 /ar( ΔPQR) = (2/3)²

48/ar( ΔPQR) = 4/9  

ar( ΔPQR) = (9 × 48)/4

ar( ΔPQR) = 9 × 12

ar( ΔPQR) = 108 cm²

Hence, the area of the larger ∆ is 108 cm²

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

$\huge\bold\pink{Solution:-}$

•Let the area of larger traingle be "x"

$\frac{area \: of \: triangle \: 1}{area \: of \: triangle \: 2} = (\frac{length \: of \: first \: triangle}{length \: of \: second \: triangle}) ^{2}$

$\frac{48}{x} = ( \frac{2}{3} ) ^{2}$

$x = \frac{48 \times 9}{4}$

X=108 cm^2