Question

Right triangle ABC is similar to right triangle DEF. If the side lengths for triangle ABC are 15, 20, 25, respectively, which values could represent the side lengths of triangle DEF

Answer 1

Answer:

$A = 15$   $B = 20$   $C = 25$

$D = 30$   $E = 40$   $F = 50$

$D = 3$    $E = 4$     $F = 5$

Step-by-step explanation:

Given

Similar Triangles: ABC and DEF

$A = 15$

$B = 20$

$C = 25$

Required

Determine the sides of DEF

No options were given, so I will solve on a general terms.

Since both triangles are similar, then the following relationship exists.

DEF = ABC * n

i.e.

$D = A * n$    $E = B * n$     $F = C * n$

Where

$n = Scale\ Factor$

Assume n = 2.

So, we have:

$D = A * n$    

$D =15 *2$

$D = 30$

$E = B * n$    

$E = 20 * 2$

$E = 40$

$F = C * n$

$F = 25 * 2$

$F = 50$

Assume $n = \frac{1}{5}.$

So, we have:

$D = A * n$    

$D =15 *\frac{1}{5}$

$D = 3$

$E = B * n$    

$E = 20 * \frac{1}{5}$

$E = 4$

$F = C * n$

$F = 25 * \frac{1}{5}$

$F = 5$

So, the possible sides are:

$A = 15$   $B = 20$   $C = 25$

$D = 30$   $E = 40$   $F = 50$

$D = 3$    $E = 4$     $F = 5$