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Relation between Inradius and Perimeter of Triangle

In a Δ ABC,...

Question

In a $Δ A B C, A D ⊥ B C$ and $C F ⊥ A B, A B = 6.4$ $c m$ , $C F = 2.6 c m$ , $A D = 3.2 c m$ . Find the (in $c m$ ) length of the side $B C$ (in $c m$ ).

4.8

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5.2

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5.6

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6.2

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Solution

The correct option is B $5.2$
Consider $△ A B C$ with $A B, C F$ as base and height respectively.

$A r e a = \frac{1}{2} \times b a s e \times h e i g h t$

$A r e a = \frac{1}{2} \times A B \times C F$

$A r e a = \frac{1}{2} \times 6.4 \times 2.6$

$A r e a = 8.32 s q . c m$

Now, consider $△ A B C$ with $B C, A D$ as base and height respectively.

$A r e a = \frac{1}{2} \times b a s e \times h e i g h t$

$A r e a = \frac{1}{2} \times B C \times A D$

$8.32 = \frac{1}{2} \times B C \times 3.2$

$B C = 5.2 c m$

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In a ΔABC,AD⊥BC and CF⊥AB,AB=6.4 cm, CF=2.6 cm, AD=3.2 cm. Find the (in cm) length of the side BC (in cm).

The correct option is B 5.2Consider △ABC with AB, CF as base and height respectively.Area=12×base×heightArea=12×AB×CFArea=12×6.4×2.6Area=8.32 sq.cmNow, consider △ABC with BC, AD as base and height respectively.Area=12×base×heightArea=12×BC×AD8.32=12×BC×3.2BC=5.2 cm

In a $Δ A B C, A D ⊥ B C$ and $C F ⊥ A B, A B = 6.4$ $c m$ , $C F = 2.6 c m$ , $A D = 3.2 c m$ . Find the (in $c m$ ) length of the side $B C$ (in $c m$ ).