Pawan is studying in IX standard. His father purchases a plot which is in a square
shape. (shown in figure). After visiting the land, few questions came in his mind. Give
answer to his questions by looking at the figure.
Answers
measure of angle AOB
Step-by-step explanation:
measure of angle a o b
Pawan is studying in IX standard. His father purchases a plot which is in a square shape. (shown in figure). After visiting the land, few questions came in his mind. Give answer to his questions by looking at the figure.
The question is incomplete. The following could be the rest of the question.
Given,
Sqare ABCD
To find,
1. Measure of angle AOB
2. If OA = 3 cm, then value of OC
3. Which is the correct congruence rule applicable to prove angle DAB = angle CBA
4. If the side of the plot is 65 m, how much wire will be needed to fence the plot all around it?
5. If the side of square is 10 cm, find the length of the diagonal AC.
Solution,
1. Since a square is a rhombus with all angles as 90∘, angle AOB = 90° because the diagonals of a rhombus are perpendicular bisectors.
2. The diagonals of a square bisect each other. So OA = OC = 3 cm.
3. To prove angle DAB = angle CBA, we must prove the congruency of triangles DAB and CBA.
In the given triangles,
DA = BC (Sides of a square are equal)
AB = AB (Common side)
DB = AC (Diagonals of a square are equal)
Therefore, triangle DAB is congruent to triangle CBA by SSS Congruence Criterion.
4. To find the wire needed to fence the plot, we must find the perimeter of the square of side 65m.
Perimeter of square = 4*side
= 4 * 65 = 260 m
Therefore, 260 metres of wire is required to fence the plot.
5. To find the length of diagonal using side = 10 cm, we can use the Pythagoras Theorem on triangle ABC.
In the right-angled triangle ABC,
AB^2 + BC^2 = AC^2
or, AC = √(AB^2 + BC^2)
AC = √(100 + 100) = √200
AC = 10√2 cm
Reference Question:
1. https://brainly.in/question/35448045?utm_source=android&utm_medium=share&utm_campaign=question
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