If height of a triangle is doubled and base is tripled then its area become __ times.

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Solution

Dear Student.

$L e t h b e t h e h e i g h t, b b e t h e b a s e a n d A_{1} b e t h e a r e a o f o r i g i n i a l t r i a n g l e . T h e n, A_{1} = \frac{1}{2} \times b \times h = \frac{b h}{2} N e w h e i g h t b e c o m e s 2 h a n d n e w b a s e b e c o m e s 3 b, t h e n a r e a A_{2} i s g i v e n b y : A_{2} = \frac{1}{2} \times 2 h \times 3 b = 3 b h I n c r e a s e i n a r e a = \frac{A_{2}}{A_{1}} = \frac{3 b h}{\frac{b h}{2}} = 3 \times 2 = 6 H e n c e t h e a r e a b e c o m e s 6 t i m e s .$

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