Answer: The answer is provided below.
Step-by-step explanation:
A rhombus has 4 equal sides, therefore, since the perimeter is 80 inches, that means each side is 20 inches.
The diagonals of a rhombus bisect one another perpendicularly, so that means there are 4 congruent right triangles that are formed.
Looking at one right triangle, we can see that the side of the rhombus will be the hypotenuse which is 20 inches. One leg is also half the longer diagonal of 16 inches.
Using Pythagorean Theorem, this will be:
x² + 16² = 20²
x² + 256 = 400
x² = 144
x = 12
Since the figure gotten is half of the shorter diagonal, then the full length of the shorter diagonal will be (12×2) = 24 inches.
The shorter diagonal of a rhombus is equal to one of its sides and the full length of the shorter diagonal will be 24 inches.
Given that,
A rhombus has a perimeter of 80 inches.
Its longer diagonal is 32 inches.
We have to find,
Explain why the shorter diagonal must be 24 inches.
According to the question,
A rhombus has 4 equal sides,
The perimeter of a rhombus is defined as either the total length of its boundaries or the sum of all four sides of it.
The perimeter is 80 inches, which means each side is 20 inches.
Diagonals bisect each other at right angles, so that means there are 4 congruent right triangles that are formed.
Then,
The side of the rhombus will be the hypotenuse which is 20 inches. One leg is also half the longer diagonal of 16 inches.
By using the Pythagoras theorem,
[tex]\rm x^2 + 16^2 = 20^2\\\\x^2 = 256 = 400\\\\x^2 = 400-256\\\\x^2 = 144\\\\x^2 = 12[/tex]
The figure gotten is half of the shorter diagonal,
then the full length of the shorter diagonal will be,
= 12×2 = 24 inches.
Hence, The shorter diagonal of a rhombus is equal to one of its sides and full length of the shorter diagonal will be 24 inches.
For more details refer to the link given below.
https://brainly.com/question/518495
