Answer:
Explanation:
Here's how you can find the length of the longer diagonal of a rhombus with sides of length 8 m and a shorter diagonal of length 10 m:
Step 1: Draw a diagram of the rhombus with the shorter diagonal labeled as 10 m.
Step 2: Draw a perpendicular bisector from one corner of the rhombus to the opposite corner, dividing the rhombus into two congruent right triangles.
Step 3: Label the longer diagonal as "d".
Step 4: Since the two congruent right triangles have sides that are half the length of the sides of the rhombus, the hypotenuse of each triangle must have length 4 m.
Step 5: Using the Pythagorean theorem, we can find the length of the other side of each triangle:
a^2 + b^2 = c^2
4^2 + b^2 = 10^2
16 + b^2 = 100
b^2 = 84
b = √84 = 2√21
Step 6: Now that we know the length of one side of each triangle, we can use it to find the length of the longer diagonal:
d^2 = 4^2 + (2√21)^2
d^2 = 16 + 168
d^2 = 184
d = √184 = 2√23
So, the length of the longer diagonal of the rhombus is 2√23 m.