The perimeter of the triangle shown is 30 inches. What is the length of the longest side of the triangle

The length of the longest side of the triangle is 13 inches

Step-by-step explanation:

step 1

Find the value of x

we know that

The perimeter of triangle is equal to the sum of its three length sides

so

we have

substitute

solve for x

step 2

Find the length of the longest side of the triangle

Remember that in a right triangle, the longest side is the hypotenuse

so

(2x+3) is the longest side

substitute the value of x

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.