Mr.Ashok has a plot of a quadrilateral shaped with vertices (0,0), (a,0), (a,b) and (0,b). He is planning to construct a beautiful house on that plot. On the basis of the above information answer the following: (i) The type of a quadrilateral shaped plot is (a) Square (b) Rhombus (c) Rectangle (d) Trapezium (ii) What will be the perimeter of a plot? (a) (a+b) units (b) 2(a+b) units (c) ab units (d) 2ab units (iii) What will be the area of a plot? (a) 0 sq.units (b) a 2 sq.units (c) b2 sq.units (d) ab sq.units (iv) The area of each triangular part of a plot will be (a) ab sq.units (b) 2ab sq.units (c) ab/2 sq.units (d) ab/4 sq.units (v) The ratio of areas of these two triangular parts of a plot will be (a) 1:2 (b) 2:1 (c) 1:1 (d) 1:4
Answers
Solution :-
(1)
Let the coordinates of given quadrilateral A(0,0), B(a,0), C(a,b) and D(0,b) .
So,
→ AB = √[(0 - a)² + (0 - 0)²] = √[(-a)² + 0] = a units
→ BC = √[(a - a)² + (b - 0)²] = √[0 + b²] = b units
→ CD = √[(0 - a)² + (b - b)²] = √[(-a)² + 0] = a units
→ DA = √[(0 - 0)² + (0 - b)²] = √[0 + b²] = b units
as we can see that,
→ AB = CD = a units
→ BC = DA = b units
since opposite sides are equal , quadrilateral shaped plot ABCD is a rectangle (c) .
(2)
→ Perimeter of plot = a + b + a + b = 2a + 2b = 2(a + b) units (b) .
(3)
→ Area of Plot = Length * Breadth = a * b = ab units² (d) .
(4)
→ Area of each each triangular part of a plot = (1/4)ab units² (d) .
(5)
→ The ratio of areas of these two triangular parts of a plot = 1 : 1 (c)
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Answer:
Step-by-step explanation:
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Answer:
QUESTION 1: (c) Rectangle
QUESTION 2: (b) 2(a+b) units
QUESTION 3: (d) ab sq. units
QUESTION 4: (c) 1/2 ab sq. units
QUESTION 5: (c) 1:1
Step-by-step explanation:
QUESTION 1: (c) Rectangle
Since the value of 'a' and 'b' are unknown and all these points when joined, they will form a closed figure with 90° [See the attached figure]
QUESTION 2: (b) 2(a+b) units
The X-Axis of points A, and D are 0, meaning
The Length of the Rectangle = a; and
The Breadth of the Rectangle = b
So, the perimeter of the rectangle = 2(l+b) nothing but 2(a+b)
QUESTION 3: (d) ab sq. units
Area of rectangle
= (l×b) [Length and Breadth shown in Q2]
= a×b
= ab sq. units
QUESTION 4: (c) 1/2 ab sq. units
A diagonal in a rectangle separates it into 2 right-angled triangles
QUESTION 5: (c) 1:1
As the 2 triangles formes will be equal.