Answer:
the hypotenuse of UVW is 7.5ft
Explanation:
the side 3ft long and the side 4.5ft long are corresponding sides
the side 4ft long and the longer leg of ΔUVW are corresponding sides
the hypotenuses of both tringles are corresponding sides
Since the given triangles are similar, their corresponding sides must be proportional and for the sides to be proportional, the shortest side of one triangle must correspond to the shortest side of the other triangle and the longest side of one triangle must correspond to the longest side of the other triangle.
Since the triangles are similar, the ratios of their corresponding sides are equal.
Step 1: Use the proportion and find the length of the longer leg of ΔUVW
long leg/4 = 4.5/3
We cross multiply
3 × long leg = 4.5 × 4
3long leg = 18
Next, we divide 3 on both sides
3long leg/3 = 18/3
Lastly, we simplify
long leg = 6
Now that we know the lengths of both legs of ΔUVW, you can use the Pythagorean formula to find the length of the hypotenuse of the triangle.
a and b = legs
c = hypotenuse
c² = a² + b²
c² = 4.5² + 6²
c² = 20.25 + 36
c² = 56.25
√c² = √56.25
c = 7.5 ft