If the sides of a triangle are 4 cm, 6 cm and 6 cm, then find the height corresponding to the smallest side.

8√2

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4√2

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16√2

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7√2

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Solution

The correct option is B
4√2

$S = \frac{P e r i m e t e r}{2} = \frac{(a + b + c)}{2} = \frac{(4 + 6 + 6)}{2} = 8 c m$

Area of the triangle = $\sqrt{s (s - a) (s - b) (s - c)}$ = $\sqrt{8 (8 - 4) (8 - 6) (8 - 6)}$ = $\sqrt{128} = 8 \sqrt{2} {c m}^{2}$

Area of a triangle is also find using $\frac{1}{2} \times b a s e \times h e i g h t$

$\Rightarrow 8 \sqrt{2} = \frac{1}{2} \times 4 \times h e i g h t$

$\Rightarrow h e i g h t = 4 \sqrt{2} c m$ .

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If the sides of a triangle are 4 cm, 6 cm and 6 cm, then find the height corresponding to the smallest side.

The correct option is B 4√2 S=Perimeter2=(a+b+c)2=(4+6+6)2=8 cm Area of the triangle =√s(s−a)(s−b)(s−c) = √8(8−4)(8−6)(8−6) = √128=8√2cm2 Area of a triangle is also find using 12×base×height ⇒8√2=12×4×height ⇒height=4√2cm.