wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the figure given below, sides PB and QA are perpendiculars drawn to the line segment AB.
If PO = 6 cm, QO = 9 cm, and area of ΔPOB=120 cm2, then find the area of ΔQOA.


Open in App
Solution

In ΔPOB and ΔQOA,

PBO=QAO=90

POB=QOA
(Since vertically opposite angles are equal)

ΔPOB ΔQOA
(by AA similarity criterion)

ar(ΔPOB)ar(ΔQOA)=PO2QO2

(The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides).

120ar(QOA)=6292

ar(QOA)=120×8136=270 cm2


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon