1.The perimeter of parallelogram QUAD is 10 more than 5 times AU. If QU =26 cm. find AU
2.If diagonals of a rhombus are 10 cm and 24 cm. find the area and perimeter of the rhombus
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where ? what?
Sure! Let's solve these problems step by step.
1. The perimeter of a parallelogram is the sum of all its sides. Let's denote the sides of the parallelogram as QU, UA, AD, and DQ.
We are given that QU = 26 cm. We need to find AU.
According to the given information, the perimeter of QUAD is 10 more than 5 times AU. Mathematically, this can be represented as:
Perimeter = 5 * AU + 10
Perimeter = QU + UA + AD + DQ
Since UA and AD are opposite sides of the parallelogram, they are equal in length. Similarly, QU and DQ are opposite sides and have the same length as well. Therefore, we can rewrite the equation as:
Perimeter = 2QU + 2UA
Perimeter = 2(26) + 2UA
Perimeter = 52 + 2UA
Since it is given that the perimeter is 10 more than 5 times AU, we can equate the two equations and solve for AU:
52 + 2UA = 5AU + 10
2UA - 5AU = 10 - 52
-3AU = -42
AU = (-42)/(-3)
AU = 14
Therefore, AU is equal to 14 cm.
2. In a rhombus, the diagonals are perpendicular bisectors of each other.
Let's denote the length of the diagonals as d1 and d2, and the side length of the rhombus as s.
The area of a rhombus can be calculated using the formula:
Area = (1/2) * d1 * d2
Given d1 = 10 cm and d2 = 24 cm, we can substitute these values into the formula to find the area:
Area = (1/2) * 10 * 24
Area = (1/2) * 240
Area = 120 cm²
The perimeter of a rhombus can be calculated using the formula:
Perimeter = 4 * s
Since all sides of a rhombus are equal, we can use either of the diagonals to find the side length.
Taking d1 as the diagonal, we can solve for s:
d1 = 2 * s
10 = 2 * s
s = 10/2
s = 5 cm
Substituting the value of s into the perimeter formula, we can find the perimeter:
Perimeter = 4 * 5
Perimeter = 20 cm
Therefore, the area of the rhombus is 120 cm² and the perimeter is 20 cm.