The perimeter of a rhombus is 20 cm. The length of one of its diagnol is 9cn.Find its area and length of other diagonal. Please solve the problem it's very urgent who will answer this question I will mark their answer brainliest and rate it too.
Answers
Answer:
Length of the another diagonal = 4.358 cm
Area of the Rhombus = 19.611 cm²
Step-by-step explanation:
( Refer to attachment for figure )
Let the length of each of the side of Rhombus be 'a' cm
Perimeter of the Rhombus = 20 cm
We know that
Perimeter of the Rhombus = 4a units
⇒ 20 = 4a
⇒ 20/4 = a
⇒ 5 = a
⇒ a = 5
One of the diagonal of the Rhombus ( d1 ) = AC = 9 cm
Let the another diagonal d2 ( BD )be 'x' cm
Consider ΔAOD
We know that
Diagonals in a Rhombus bisect each other perpendicularly
- AO = OC = AC/2 = 9/2 = 4.5 cm
- OD = BO = BD/2 = x/2 cm
- AC ⊥ BD ⇒∠AOD = 90°
So, ΔAOD is a Right angled triangle
By Pythagoras theorem
⇒ AO² + OD² = AD²
⇒ 4.5² + ( x/2 )² = 5²
⇒ 20.25 + x²/4 = 25
⇒ x²/4 = 25 - 20.25
⇒ x²/4 = 4.75
⇒ x² = 4.75 × 4
⇒ x² = 19
⇒ x = √19
⇒ x = 4.358
Therefore the length of the another diagonal is 4.358 cm
Area of the Rhombus = d1 × d2 / 2
= 9 × 4.358 / 2
= 4.5 × 4.358
= 19.611 cm²
Therefore the area of the Rhombus is 19.611 cm²
- Digonal of a rhombus bisect each other.That means each diagonal cuts the other in two equal parts.
- Area of rhombus:- Let diagonal are d1 and d2
Area = 1/2 d1 × d2
See figure
Given perimeter is 20 cm
we know sides are equal
(side )×4 = 20
or, side = 5 cm
In right ∆A0B
By Pythagoras theorem
=
= 25 -20.25=4.75
=
d2 = 2× 2.17=4.34 cm
Now area = 1/2 ×d1 × d2
1/2 × 9 × 4.34
19.53 square cm
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