Question

In each of the figures [(i)-(iv)] given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in each of the following :
(i)
(ii)
(iii)
(iv)

Answer 1

SOLUTION :

BASIC PROPORTIONALITY THEOREM (BPT)  is used in this question .

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.

This theorem also known as ‘Thales theorem’.

(i) 1/c =d/x

x×1 = c×d    (by cross multiplication)

x = cd  

Hence, the value of x is cd .

(ii)  a/1 = b/x  

a × x = b × 1   (by cross multiplication)

x = b/a  

Hence, the value of x is b/a.

(iii) g/x = 1/g  

g × g = x × 1   (by cross multiplication)

g² = x  

Hence, the value of x is g².

(iv) 1/x = h/1

x × h = 1   (by cross multiplication)

x = 1/h  

Hence, the value of x is 1/h .

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Answer 2

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