Question

2 points
1.
Sides of two similar triangles are in
the ratio 3:15. Areas of these triangles are in
the ration
9:225
30:50
9:25
5:3​

Answer 1

Ratio of their areas is 16:81.

Explanation:

Let us have two similar triangles ΔABC and ΔDEF as shown below. As they are similar, we have

ABDE=ACDF=BCEF

Let us also draw perpendiculars AP and DQ from A and D respectively on to BC and EF as shown.

It is apparent that ΔAPB and ΔDEQ are also similar as all respective angles are equal. Hence,

ABDE=APDQ=BPEQ

We also have ΔABC=12×BC×AP and ΔDEF=12×EF×DQ and

ΔAPBΔDEQ=BC×APEF×DQ=BCEF×APDQ

But APDQ=ABDE=BCEF and hence

ΔAPBΔDEQ=BCEF×BCEF=BC2EF2 and as

BCEF=ACDF=ABDE

ΔAPBΔDEQ=AC2DF2=BC2EF2=AB2DE2

Hence if sides of two similar triangles are in the ratio a:b, their areas are in the proportion a2:b2

As in given case sides are in the ratio of 4:9.

ratio of their areas is 42:92 or 16:81.

see fig. in the attachment ☺️