In the above figure- find the value of X-A- 4 cmB- 12 cmC- 20 cmD- 8 cm

The correct option is D 8 cm We can see that, ABC ∼ DEF by AAA Similiarity Criterion ⇒AB/DE = BC/EF By Pythagoras theorem, we have BC = √(AC ^2 AB ^2) = √(5^2 ...

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Standard IX

Mathematics

Proportion in Similar Triangles

In the above ...

Question

In the above figure , find the value of $x$ .

4 cm

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8 cm

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12 cm

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20 cm

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Solution

The correct option is B
8 cm

We can see that, $△ A B C \sim △ D E F$ by AAA Similiarity Criterion

$\Rightarrow \frac{A B}{D E} = \frac{B C}{E F}$

By Pythagoras theorem, we have $B C = \sqrt{A C^{2} - A B^{2}}$ = $\sqrt{5^{2} - 3^{2}} = \sqrt{16} = 4$ cm

$\Rightarrow \frac{3}{6} = \frac{4}{E F}$

$\Rightarrow E F \times 3 = 6 \times 4$

Thus EF = 8 cm

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In the above figure , find the value of x.

The correct option is B 8 cm We can see that, △ABC∼△DEF by AAA Similiarity Criterion ⇒ABDE=BCEF By Pythagoras theorem, we have BC=√AC2−AB2 = √52−32=√16=4 cm ⇒36=4EF ⇒ EF×3=6 ×4 Thus EF = 8 cm

In the above figure , find the value of $x$ .