Question

Corresponding sides of two similar triangles are in the ratio 4:9 Areas of these triangles are in the ration (a) 2:3 (b) 4:9 (c) 9:4 (d) 16:81

Answer 1

D will be the answer of this question

Answer 2

Answer:

$(d) \ \bold{16:81}$

Step-by-step explanation:

$The altitudes to the corresponding sides of two similar triangles have the same ratio of the corresponding sides. \\ \\ Here, the corresponding sides are in the ratio 4:9. \\ \\ If we draw altitudes perpendicular to these sides, their ratio will also be 4:9. \\ \\ Let the corresponding sides be \ 4x\ and \ 9x. \\ \\ And let the altitudes be \ 4h\ and \ 9h.$

$Ratio of areas \\ \\ = \frac{1}{2} \times 4x \times 4h : \frac{1}{2} \times 9x \times 9h \\ \\ = \frac{1}{2} \times 16xh : \frac{1}{2} \times 81 xh \\ \\ = \frac{1}{2}xh \times 16 : \frac{1}{2}xh \times 81 \\ \\ = \bold{16:81} \\ \\ \\ \therefore\ Option (d) is the answer.$

$Hope this may be helpful. \\ \\ Thank you. Have a nice day. \\ \\ \\ \#adithyasajeevan$