Question

the areas of two similar triangles are 144cm2 and 81cm2. if one median of the first triagle is 16cm,find the length of corresponding median of the second triangle.

Answer 1

Answer:

The length of median of second triangle is 9 cm

Step-by-step explanation:

$\text{Given the areas of two similar triangles are }144cm^2\text{ and }81cm^2$

$\text{If one median of the first triangle is 16cm, then}$

we have to find the length of corresponding median of the second triangle.

By area of similar triangle theorem

The ratio of area of two similar triangles is equal to the square of ratio of length of median of two triangles i.e

$\frac{\text{Area of first triangle}}{\text{Area of second triangle}}=(\frac{\text{length of median of first triangle}}{\text{length of median of second triangle}})^2$

$\frac{144}{81}=\frac{16}{x}$

$x=16\times \frac{81}{144}=9 cm$

The length of median of second triangle is 9 cm

Answer 2

Answer:

Let two triangle are ABC and DEF

Given ΔABC ∼ ΔDEF

=> Area of ΔABC/Area of Δ DEF = AM2 /DN2

=> 144/81 = 162 /DN2

=> 144/81 = 256 /DN2

=> DN2 = (256*81)/144

=> DN = √{(256*81)/144}

=> DN = (16*9)/12

=> DN = (4*9)/3

=> DN = 4*3

=> DN = 12 cm