Q22 of 180 Page 1

The line segment XY is parallel to side AC of ΔABC and it divides the triangle into two parts of equal area. Prove that AX : XB = (√2 – 1) : 1.

OR


In a trapezium ABCD, O is the point of intersection of AC and BD, AB || CD and AB = 2 × CD. If the area of ΔAOB is 84 cm2, find the area of ΔCOD.


The diagram is shown below.



In this diagram, area (BXY) = area (XYAC) = area (ABC)


⇒ ∠BXY = ∠BAC and ∠BYX = ∠BCA as they are corresponding angles.


⇒ ΔBXY ∼ ΔBAC


Using theorem, the ratio of areas of two similar triangles is equal to the ratio of square of the corresponding sides.


⇒


⇒


⇒


To find,




∴ ratio is (√2 – 1) : 1


Hence, proved.


OR


The diagram is shown below.



⇒ ∠AOB = ∠DOC as they are vertically opposite angles


⇒ ∠ODC = ∠OBA as they are alternate angles


⇒ ΔCOD ∼ ΔAOB [By AA similarity criterion]


Using theorem, the ratio of areas of two similar triangles is equal to the ratio of square of the corresponding sides.


⇒


But AB = 2DC


⇒


∴ area (DCO) = 21 cm2


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20

A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained


(i) Mean height (in cm) of the girls is


(a) 146.8


(b) 147.8


(c) 148.8


(d) 149.8


(ii) The commutative frequency table is useful in determining the


(a) Mean


(b) Median


(c) Mode


(d) All of these


(iii) Lower limit of the median class is


(a) 130


(b) 140


(c) 150


(d) None of the above


(iv) Sum of lower limit of median class and modal class is


(a) 270


(b) 290


(c) 310


(d) None of these


 21

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 23

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 24

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