Question

The areas of two similar triangles are $169 cm^{2}$ and $121 cm^{2}$respectively. If the longest side of the larger triangle is 26 cm, what is the length of the longest side of the smaller triangle?

Answer 1

Answer:

The length of the longest side of the smaller triangle is 22 cm.

Step-by-step explanation:

Given:

Let the two triangles be ΔABC & ΔPQR.

ΔABC ~ ΔPQR.

Area of ΔABC = 169 cm ²

Area of ΔPQR = 121 cm².

The longest side(BC) of ΔABC is 26 cm .

Let QR is the longest side 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.]

169/121 = (26/QR)²

26/QR = √169/121

26/QR = 13/11

13 QR = 26 × 11

QR = (26 × 11)/13

QR = 2 × 11

QR = 22 cm

Hence, the length of the longest side of the smaller triangle is 22 cm.

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

169/121=(26×26)/x×x

=>13/11=26/x

=>X=(26×11)/13

=22cm=longest side of smaller triangle