In quadrilateral ABCD m ACD =2 x+4 and m ACB=5x-11. for what value of x is ABCD a rhombus?
1 answer:
The value of x is 5
Explanation
Given <ACD=2x+4
<ACB=5x-11
Given that ABCD is a rhombus. So the opposite angles will be same and all the sides will be equal.
diagonal AC divides the rhombus into two triangles ACD and ACB
according to angle sum property, the sum of all angles of a triangle is 180.
consider triangle ACD
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Answer:
B) 28.53 unit²
Step-by-step explanation:
The diagonal AD divides the quadrilateral in two triangles:
- Triangle ABD
- Triangle ACD
Area of Quadrilateral will be equal to the sum of Areas of both triangles.
i.e.
Area of ABCD = Area of ABD + Area of ACD
Area of Triangle ABD:
Area of a triangle is given as:
Base = AB = 2.89
Height = AD = 8.6
Using these values, we get:
Thus, Area of Triangle ABD is 12.43 square units
Area of Triangle ACD:
Base = AC = 4.3
Height = CD = 7.58
Using the values in formula of area, we get:
Thus, Area of Triangle ACD is 16.30 square units
Area of Quadrilateral ABCD:
The Area of the quadrilateral will be = 12.43 + 16.30 = 28.73 units²
None of the option gives the exact answer, however, option B gives the closest most answer. So I'll go with option B) 28.53 unit²