Question

if two Triangles have equal area and the ratio of their bases is equal to 2 ratio 3 then the ratio of their corresponding altitudes is

Answer 1

Let AB = 2x. and PQ = 3x.

Now area ( ABC ) = 1/2 2x AD
area ( PQR ) = 1/2. 3x. RS

as area is equal.
1/1 = 2AD / 3RS
3RS = 2AD

thus ratio of corresponding altitude s will be. = 3/2.



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Answer 2

The the ratio of their corresponding altitudes is 3 : 2.

Step-by-step explanation:

Let the base and height of first triange = 2x and h and

Let the base and height of second triange = 3x and H and

To find, the the ratio of their corresponding altitudes = ?

∴ The area of first triangle $=\dfrac{1}{2}\times 2x \times h$

and  

The area of second triangle $=\dfrac{1}{2}\times 3x \times H$

According to question,

The area of first triangle =The area of second triangle

⇒ $\dfrac{1}{2}\times 2x \times h=\dfrac{1}{2}\times 3x \times H$

⇒ $2 \times h=3 \times H$

⇒ $\dfrac{h}{H}=\dfrac{3}{2}$

Hence, the the ratio of their corresponding altitudes is 3 : 2.