Answer:
Step-by-step explanation:
All three triangles in the picture are right triangles so we can use the Pythagorean theorem which states:
The square of the hypotenuse is the sum of the squares of the other two sides
- In the outer triangle,
the hypotenuse has a length = 8 + 4 = 12
The legs of the right triangle are y and z
So using the Pythagorean theorem:
y² + z² = 12² [1]
- For the inner triangle on the right, hypotenuse = z, legs are x and 8:
z² = x² + 8² [2]
- For the right inner triangle, hypotenuse = y, legs are x and 4:
y² = x² + 4² [3]
- Substituting for z² and y² in equation 1 from [2] and [3]
(x² + 8²) + (x² + 4²) = 12²
x² + 8² + x² + 4² = 12²
x² + x² + 64 + 16 = 144
2x² + 80 = 144
2x² = 144 - 80 => subtract 80 both sides
2x² = 64
x² = 64/2
x² = 32
- Using equation [3] , y² = x² + 4²
y² = 32 + 4²
y² = 32 + 16
y² = 48
y = √48 = 6.9
- Answer y = 6.9
