To construct a triangle similar to given - ABC with its sides 35 of that of - ABC- a ray BX is drawn at acute angle with BC- How many minimum no- of points should be marked on BX-

The correct option is D 5 Suppose PQB is the required triangle. BQ = 35 × BC⇒ PQ = 35× (BQ+QC) ⇒ 5BQ = 3BQ+3CQ⇒ 2BQ = 3CQ , i.e, BQCQ = 32 ...

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Standard X

Mathematics

Constructing a Similar Triangle with a Scale Factor

To construct ...

Question

To construct a triangle similar to given $Δ A B C$ with its sides $\frac{3}{5}$ of that of $Δ A B C$ , a ray $B X$ is drawn at acute angle with $B C$ . How many minimum no. of points should be marked on $B X$ ?

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Solution

The correct option is D $5$
Suppose $△ P Q B$ is the required triangle.
$B Q = \frac{3}{5} \times B C \Rightarrow P Q = \frac{3}{5} \times (B Q + Q C) \Rightarrow 5 B Q = 3 B Q + 3 C Q \Rightarrow 2 B Q = 3 C Q$ , i.e, $\frac{B Q}{C Q} = \frac{3}{2}$
Therefore, $Q$ divides $B C$ in ratio $3 : 2$ . So, minimum number of points required on ray $B X = 2 + 3 = 5$

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To construct a triangle similar to given ΔABC with its sides 35 of that of ΔABC, a ray BX is drawn at acute angle with BC. How many minimum no. of points should be marked on BX?

The correct option is D 5Suppose △PQB is the required triangle.BQ=35×BC⇒PQ=35×(BQ+QC)⇒5BQ=3BQ+3CQ⇒2BQ=3CQ, i.e, BQCQ=32Therefore, Q divides BC in ratio 3:2. So, minimum number of points required on ray BX=2+3=5

To construct a triangle similar to given $Δ A B C$ with its sides $\frac{3}{5}$ of that of $Δ A B C$ , a ray $B X$ is drawn at acute angle with $B C$ . How many minimum no. of points should be marked on $B X$ ?