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Standard VII

Mathematics

Pythagorean Theorem

For the given...

Question

For the given diagram, if $A B : B C = 5 : 13$ and $A C = 14$ units, then $B C =$ units.

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Solution

The correct option is A $13$
For the given triangle $A B C$ , $A B : B C = 5 : 13$ and $A C = 14$ units.
Let $x$ be a common factor
$\Rightarrow A B = 5 x & B C = 13 x$
Now, Using pythagoras theorem:
$A B^{2} + B C^{2} = A C^{2}$
$\Rightarrow 14^{2} = (5 x)^{2} + (13 x)^{2}$
$\Rightarrow 25 x^{2} + 169 x^{2} = 196$
$\Rightarrow 196 x^{2} = 196 \Rightarrow x^{2} = 1 \Rightarrow x = 1$
$∴ B C = 13 x = 13$ units

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For the given diagram, if AB:BC=5:13 and AC=14 units, then BC= units.

The correct option is A 13For the given triangle ABC, AB:BC=5:13 and AC=14 units. Let x be a common factor ⇒AB=5x & BC=13x Now, Using pythagoras theorem: AB2+BC2=AC2 ⇒142=(5x)2+(13x)2 ⇒25x2+169x2=196 ⇒196x2=196⇒x2=1⇒x=1 ∴BC=13x=13 units

For the given diagram, if $A B : B C = 5 : 13$ and $A C = 14$ units, then $B C =$ units.