Mathematics
In figure (3) given below, ABCD is a rhombus. Find x and y.
![In figure (3) given below, ABCD is a rhombus. Find x and y. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q5c-c13-1-rectilinear-ml-aggarwal-solutions-icse-class-9-1200x958.png)
Rectilinear Figures
ICSE
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Answer
Sides of rhombus are equal.
∴ AB = AD
⇒ 4x - 4 = 3x + 2
⇒ 4x - 3x = 2 + 4
⇒ x = 6.
AB = 3x + 2 = 3(6) + 2 = 20.
In △ABD,
AB = AD
so, ∠D = ∠B (Angles opposite to equal sides are equal in isosceles triangle)
Let angle be ∠D = ∠B = a
So,
⇒ ∠A + ∠D + ∠B = 180°
⇒ 60° + a + a = 180°
⇒ 2a = 180° - 60°
⇒ 2a = 120°
⇒ a = 60°.
Hence, △ABD is an equilateral triangle, so all sides are equal.
⇒ BD = AB
⇒ y - 1 = 20
⇒ y = 21.
Hence x = 6 and y = 21.
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