Question

Please answer quickly!

Fill in the blanks:

triangle ABC and triangle DEF are similar. Area of ABC is 9cm2 and Area of DEF is 64cm2. If DE = 5.1cm, then the value of AB is _____.

Answer 1

Answer:

ar ABC / ar Def

= ab sq / de sq

3/8=ab/5.1

ab=153/80

1.9

Answer 2

AB = 1.192 cm

Step-by-step explanation:

Given:

Here ΔABC and ΔDEF are similar.

Area of ABC = 9 $cm^2$ and Area of DEF is 64 $cm^2$.

Also, DE = 5.1 cm , AB = ?

We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

⇒ $\frac{ar(\triangle BAC)}{ar(\triangle EDF)} =\frac{AB^2}{DE^2}$

⇒ $\frac{9}{64} =\frac{AB^2}{5.1^2}$

⇒ $AB^2=\frac{9\times 26.01}{64}$

⇒ $AB^2=\frac{234.09}{64}$

⇒ $AB^2 = 3.65$

$AB = \sqrt{3.65}$

AB = 1.192 cm