Question

∆ ABC ~∆ DEF and their areas are respectively 49cm^2 and 100cm^2.if DE=17.5cm,then find AB​

Answer 1

Answer:

The value of AB is 12.25 cm

Answer 2

AB = 12.25 cm

Step-by-step explanation:

∆ ABC ~∆ DEF

using the theorem

"The ratio of the areas of two similar triangles is equal to the square of the ratio of any pair of their corresponding sides".

therefore

$\frac{area of triangle ABC}{area of triangle FED}$ = $\frac{AB^2}{DE^2}$

= $\frac{49}{100 } = \frac{AB^2}{17.5 ^2}$

= (17.5)² ×49 = AB²×100

$AB^2 = \frac{306.25 \times 49}{100}\\\\AB^2 = \frac{15006.25}{100}\\AB^2 = 150.0625\\AB = \sqrt{ 150.0625} \\AB = 12.25$

hence ,

AB = 12.25 cm

#Learn more:

∆ABC ~ ∆ DEF, ar ( ∆DEF ) = 100cm*cm and AB/DE=1/2​

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