Question

The area of two similar triangles are 36 $cm^{2}$ and 100 $cm^{2}$. If the length of a side of the smaller triangle in 3 cm, find the length of the corresponding side of the larger triangle.

Answer 1

Answer:

The length of the corresponding side of the larger triangle of ΔPQR is 5 cm

Step-by-step explanation:

Given:

Let the two triangles be ΔABC & ΔPQR.

ΔABC ~ ΔPQR.

Area of ΔABC = 36 cm ²

Area of ΔPQR = 100 cm².

The length of a  side(BC) of a Smaller  ΔABC is 3 cm .

Let QR be the length of the corresponding side of the larger triangle of ΔPQR.

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.]

36/100 = (3/QR)²

3/QR = √36/100

3/QR = 6/10

6 QR = 3 × 10

QR = (3 × 10)/6

QR = 10 /2

QR = 5  cm

Hence, the length of the corresponding side of the larger triangle of ΔPQR is 5 cm

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

Answer

Smaller triangle = 3cm

larger triangle = 4 cm

The linear scale factor = 3/4 = 0.75

Area scale factor = 0.75 × 0.75 = 0.5625

Let area of smaller triangle be x.

Then area scale factor = x / 48

X/48 = 0.5625

X = 0.5625 × 48 = 27

= 27 square centimeters