Step-by-step explanation:
these are all right-angled triangles. even the smallest one with the x side.
so, we need to apply Pythagoras to get the missing sides and finally x.
c² = a² + b²
c is the Hypotenuse, the baseline of the triangle opposite of the 90 degree angle. a and b are the legs of the triangle enclosing the 90 degree angle.
so,
52² = 48² + side1²
2704 = 2304 + side1²
400 = side1²
side1 = 20
20² = 12² + side2²
400 = 144 + side2²
256 = side2²
side2 = 16
13² = 5² + (larger part of side2)²
169 = 25 + (larger part of side2)²
144 = (larger part of side2)²
larger part of side2 = 12
that means the smaller part of side 2 = 16-12 = 4.
x² = 5² + 4² = 25 + 16 = 41
x = sqrt(41)
So, D is the right answer option.
