Question

1. parallelogram mnpq is shown below with diagonals and intersecting at point r. which of the following would not be sufficient information to show that mnpq is a rhombus? (1) (2) nmpqpm (3) (4) qmpqpm 12. the diagonals of a rhombus have lengths of 18 cm and 10 cm. which of the following would be closest to the perimeter of this rhombus? (1) 34.4 cm (2) 39.1 cm (3) 41.2 cm (4) 44.5 cm

Explanation:

Step1: Split diagonals in half

Diagonals of a rhombus bisect each other, so:
$\frac{18}{2}=9$ cm, $\frac{10}{2}=5$ cm

Step2: Calculate side length via Pythagoras

Side $s$ of rhombus:
$$s=\sqrt{9^2 + 5^2}=\sqrt{81+25}=\sqrt{106}\approx10.30$$

Step3: Compute perimeter of rhombus

Perimeter $P = 4s$:
$P=4\times10.30=41.2$ cm

Answer:

(3) 41.2 cm

---
Note: Question 11 has incomplete options, so it cannot be solved. Please provide full details for question 11 if you need assistance with it.