Which of the following could NOT be the lengths of the sides of a triangle? A.5 in, 5 in, 5 in
B. 10 cm, 15 cm, 20 cm
C. 3 in, 4 in, 5 in
D. 8 ft, 15 ft, 5 ft

Given:

Sides of triangles in the options.

To find:

Which could NOT be the lengths of the sides of a triangle.

Solution:

Condition for triangle:

Sum of two smaller sides of a triangle must be greater than the longest side.

In option A,

Sides 5 in, 5 in, 5 in are the lengths of the sides of a triangle.

In option B,

Sides 10 cm, 15 cm, 20 cm are the lengths of the sides of a triangle.

In option C,

Sides 3 in, 4 in, 5 in are the lengths of the sides of a triangle.

In option D,

Since, the sum of two smaller sides is less than the longest side, therefore the sides 8 ft, 15 ft, 5 ft are not the lengths of the sides of a triangle.

Therefore, the correct option is D.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions