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
SOlutions pleaseeeeeee
I got it!The area is 120 sq cm and the perimeter is 52 cm
Reiny and others, answer no.1 please!
Sure! Let's solve each problem step by step:
Problem 1:
Let's break down the given information:
The perimeter of parallelogram QUAD is 10 more than 5 times AU.
QU = 26 cm.
To find AU, we can set up an equation based on the information given.
The formula for the perimeter of a parallelogram is P = 2(AU + QU), where P is the perimeter.
Given that the perimeter is 10 more than 5 times AU, we can write the equation as:
2(AU + 26) = 5AU + 10
Now, we can solve this equation to find the value of AU:
2AU + 52 = 5AU + 10
2AU - 5AU = 10 - 52
-3AU = -42
AU = -42 / -3
AU = 14
So, AU is equal to 14 cm.
Problem 2:
Let's break down the given information:
The diagonals of a rhombus are 10 cm and 24 cm.
To find the area and perimeter of a rhombus, we need some additional information. The formulae for area and perimeter of a rhombus are as follows:
Area = (diagonal1 × diagonal2) / 2
Perimeter = 4 × side length
Since the diagonals are given, we can use these formulas to find the area and perimeter of the rhombus.
Given that the diagonals are 10 cm and 24 cm, we can plug these values into the formulae:
Area = (10 cm × 24 cm) / 2 = 240 cm²
The area of the rhombus is 240 cm².
Now, let's find the side length. We can use the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.
Considering the rhombus, we have two congruent right triangles formed by the diagonals. The hypotenuse of each triangle is a side of the rhombus.
Let's denote the side length as "s":
Using the Pythagorean theorem, we have:
(s/2)² + (s/2)² = (24/2)²
(s²/4) + (s²/4) = 12²
2s²/4 = 144
2s² = 576
s² = 288
s = √288
s ≈ 16.97 cm
Now that we know the side length (approximately 16.97 cm), we can calculate the perimeter:
Perimeter = 4 × side length = 4 × 16.97 cm ≈ 67.88 cm
So, the area of the rhombus is 240 cm², and the perimeter is approximately 67.88 cm.