Answer:
x = 48
Step-by-step explanation:
To solve this problem, one must assume that the segment with a length of (7) bisects the segment with a length of (x).
It is given that the segment with a length of (7) is perpendicular (forms a right angle with) the segment that has a length of (x). This is indicated by the box around one of the angles, signifiying that it is a right angle, or (90) degree angle. Therefore, the triangle with sides measuring (25) and (7) is a right triangle. Thus, one can use the Pythagorean theorem to solve for the base length. Then multiply it by (2) to find the total length of (x).
The Pythagorean theorem states the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs, or sides adjacent to the right angle, and (c) is the hypotenuse or side opposite the right angle.
[tex]a^2+(7)^2=(25)^2[/tex]
Simplify,
[tex]a^2+49=625[/tex]
Inverse operations,
[tex]a^2=576\\\\a=24[/tex]
Multiply this value by (2) to find the total side length of the segment (x),
2(a)
Substitute,
2(24)
Simplify,
48
