RICE is a rhombus. Find x, y, z. Justify your findings. Hence, find the perimeter of the rhombus.
Solution:
Given, RICE is a rhombus.
We have to find the value of x, y and z.
The diagonals of a rhombus bisect each other.
So, OE = OI
5 = x + 2
x = 5 - 2
x = 3 cm
Similarly, OC = OR
12 = y + x
12 = y + 3
y = 12 - 3
y = 9 cm
Considering triangle EOR,
EOR is a triangle right angled at O.
ER² = OE² + OR²
z² = 5² + 12²
z² = 25 + 144
z² = 169
Taking square root,
z = 13 cm
Therefore, the values of x, y and z are 3 cm, 9 cm and 13 cm.
We have to find the perimeter of the rhombus.
We know, perimeter = sum of all sides
The sides of a rhombus are equal.
So, perimeter of rhombus = 4(side)
= 4(13)
= 52 cm
Therefore, the perimeter of the rhombus is 52 cm.
✦ Try This: A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a __________. (a) rhombus, (b) parallelogram, (c) square, (d) rectangle
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 37
RICE is a rhombus. Find x, y, z. Justify your findings. Hence, find the perimeter of the rhombus
Summary:
RICE is a rhombus. The values of x, y, z are 3 cm, 9 cm and 13 cm. The perimeter of the rhombus is 52 cm.
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