The lengths of diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus. 10. In a parallelogram ABCD find the measure of all the angles if one its angles is 15° less than twice the smallest angle.
Answers
Answer:
(i) First we will Half it's both diagonals than we will get 12 cm and 9 cm respectively.
Now we will apply pythagoras theorem by taking one side of the rhombus as hypotenuse which we will take as x and half of both diagonals as base and height
(12 cm)² + (9 cm)² = (x)²
144 cm² + 81 cm² = (x)²
225 cm² = (x)²
x = 15 cm
Therefore, one side of the rhombus will be 15 cm.
(ii) Let the larger angle of the parallelogram be 2x-15° and smaller angle be x; then
We know that sum of all four angles of a parallelogram is 360° and the opposite angles and are equal; then
2x-15°+x+2x-15°+x=360°
6x-30°=360°
6x=390°
x=65°
Therefore the angles are 115°, 65°, 115°, 65°
Step-by-step explanation:
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