200k views
2 votes
Rhombus ABCD has perimeter 148, and one of its diagonals has length 24. How long is the other diagonal?

2 Answers

3 votes

Answer:

70

Explanation:

The four sides of a rhombus all have equal length, so if the perimeter is 148, then each side has length 148/4 = 37. Also, the diagonals of a rhombus bisect each other at right angles, so the diagonal of length 24 is cut into two pieces of length 12. We can show this information in a diagram (shown below.)

Applying the Pythagorean Theorem to any of the four right triangles in our diagram, we have

12² + x² = 37².

Solving this equation for positive x, we get x = √37² - 12² = √1369 - 144 = √1225 = 35. The length of the long diagonal is x + x = 70.

Rhombus ABCD has perimeter 148, and one of its diagonals has length 24. How long is-example-1
User Uasthana
by
8.3k points
2 votes

Answer:

70 units.

Explanation:

The 4 sides of a rhombus are equal so each side has length 148 /4

= 37 units. The diagonals bisect each other at right angles so when we draw the 2 diagonals we have 4 congruent right-angled triangles.

So consider one of these triangles:

The hypotenuse is 37 units and one of the legs = 1/2 * 24 = 12 units ( half of the diagonal of length 24).

So the other leg is found using Pythagoras:

x^2 = 37^2 - 12^2 = 1225

x = 35.

This is half of the other diagonal so the latter = 70 units.

User Kmiklas
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories