Question

Triangles ABC and d e f are similar the lengths of the sides of ABC are 56/64 and 72 the length of the largest side of d e f is 252 what is the length of the smallest side of d e f

Answer 1

Answer:

$D E F = 196$

Step-by-step explanation:

Given

$ABC = 56, 64\ and\ 72$

$Largest\ of\ D E F = 252$

Required

Determine the smallest side of DEF

Since both sides are similar, then the sides of DEF can be calculated using:

$D E F = k * ABC$

First, we need to solve for k

From the given parameters

$D E F = 252$ when $ABC = 72$

This is so because these are the largest sides of both triangles respectively

$D E F = k * ABC$

$252 = k * 72$

Divide through by 72

$252/72 = k * 72/72$

$k=252/72$

$k=3.5$

We make use of the same formula to determine the length of the smallest side.

The smallest of ABC is 56, so we have:

$D E F = k * ABC$

$D E F = 3.5 * 56$

$D E F = 196$

Hence, the smallest side of DEF is 196