Question

The corresponding sides of ΔABC and ΔDEF have equal lengths. The area of ΔABC is 4 square units, and the longest side of ΔDEF is 5 units long. What is the area of ΔDEF? 2 square units 4 square units 10 square units 20 square units

Answer 1

if the corresponding sides are equal the 2 triangles are congruent ( by SSS) so their areas are the same
so area of triangle DEF = 4 sq units

Answer 2

The area of ΔDEF is
`4\ units^(2)`

Explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

and

The ratio of its areas is equal to the scale factor squared

In this problem

The corresponding sides of ΔABC and ΔDEF have equal lengths

therefore

the scale factor is equal to
`1`

The triangles are congruent

therefore

ΔABC and ΔDEF has the same area