If R, S, equals, 62RS=62, S, Q, equals, 64SQ=64, R, Q, equals, 76RQ=76, V, T, equals, 32VT=32, and U, T, equals, 38UT=38, find the perimeter of triangle, T, U, V△TUV. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale
To find the perimeter of triangle TUV, we need to find the lengths of all three sides and then add them together.
From the given information, we know the following:
UT = 38
VT = 32
To find TU, we can use the Pythagorean theorem because triangle TUV is a right triangle.
Let UT = x, VT = y, and TU = z.
We have:
x^2 + y^2 = z^2
38^2 + 32^2 = z^2
1444 + 1024 = z^2
2468 = z^2
z ≈ 49.7
Therefore, the lengths of the sides of triangle TUV are:
UT = 38
VT = 32
TU = z ≈ 49.7
The perimeter of triangle TUV is:
38 + 32 + 49.7 ≈ 119.7
Therefore, the perimeter of triangle TUV is approximately 119.7.