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36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is (a) 12 units (b) 26 units (c) 24 units (d) 36 units

The correct answer is (b) 26 units Solution From the given details we note that area of rectangle = 36 units2 36 can be written as... View Article

A rectangular piece of dimensions 3 cm × 2 cm was cut from a rectangular sheet of paper of dimensions 6 cm × 5 cm (Fig. 9.14). Area of remaining sheet of paper is (a) 30 cm2 (b) 36 cm2 (c) 24 cm2 (d) 22 cm2

The correct answer is (c) 24 cm2 Justification Let us calculate the area of rectangular piece = length × breadth = 2 cm... View Article

Observe the shapes 1, 2, 3 and 4 in the figures. Which of the following statements is not correct? (a) Shapes 1, 3 and 4 have different areas and different perimeters. (b) Shapes 1 and 4 have the same area as well as the same perimeter. (c) Shapes 1, 2 and 4 have the same area. (d) Shapes 1, 3 and 4 have the same perimeter.

The correct answer is (a) Shapes 1, 3 and 4 have different areas and different perimeters. Justification Shape 1 Perimeter = 1 + 1 + 1 + 1... View Article

It is possible to have a triangle in which two angles are acute. State whether the statement is True or False.

The given statement is False Justification A triangle can never have only one acute angle. If a triangle has 1 acute angle, the other angles... View Article

It is possible to have a triangle in which two of the angles are obtuse. State whether the statement is True or False.

The given statement is False Justification A triangle cannot have two obtuse angles According to the angle sum property, the sum... View Article

It is possible to have a triangle in which two of the angles are right angles. State whether the statement is True or False.

The given statement is False Justification A triangle cannot have more than one or two 90 degrees or right angles, because by the angle sum... View Article

If M is the mid-point of a line segment AB, then we can say that AM and MB are congruent. State whether the statement is True or False.

The given statement is True Justification From the figure, we observe that M is the midpoint, So, AM = MB... View Article

It is possible to have a right-angled equilateral triangle. State whether the statement is True or False.

The given statement is False Justification In a right angled triangle, sum of squares of two sides is equal to the square of the third side.... View Article

The sum of the measures of three angles of a triangle is greater than 180o. State whether the statement is True or False.

The given statement is False Justification The sum of the measures of three angles of a triangle is equal to 180o. The angle sum property of... View Article

Sum of any two angles of a triangle is always greater than the third angle. State whether the statement is True or False.

The given statement is False Justification The Sum of any two angles of a triangle is either greater than the third angle or smaller than... View Article

In ∆ABC, AB = 3.5 cm, AC = 5 cm, BC = 6 cm and in ∆PQR, PR= 3.5 cm, PQ = 5 cm, RQ = 6 cm. Then ∆ABC ≅ ∆PQR. State whether the statement is True or False.

The given statement is False Justification In ∆ABC AB = 3.5 cm AC = 5 cm BC = 6 cm In ∆PQR PR= 3.5 cm PQ = 5 cm RQ = 6 cm. Then ∆ABC ≅ ∆PRQ... View Article

The difference between the lengths of any two sides of a triangle is smaller than the length of third side. State whether the statement is True or False.

The given statement is True Justification The sum of the lengths of any two sides of a triangle is always greater than the length of the... View Article

Sum of two sides of a triangle is greater than or equal to the third side. State whether the statement is True or False.

The given statement is False Justification The sum of the lengths of any two sides of a triangle is always greater than the length of the... View Article

In a triangle, sum of squares of two sides is equal to the square of the third side. State whether the statement is True or False.

The given statement is False Justification In a right angled triangle, sum of squares of two sides is equal to the square of the third side.... View Article

In figure, (i) ∠ TPQ = ∠ ___ + ∠ _ (ii) ∠ UQR = ∠ _ + ∠ _ (iii) ∠ PRS = ∠ _ + ∠ ___

Solution From the figure, we observe that From exterior angle property (i) ∠ TPQ = ∠ PQR + ∠ PRQ (ii) ∠ UQR = ∠... View Article

In figure AB = AD and ∠BAC = ∠ DAC. Then (i) ∆ ≅ ∆ ABC. (ii) BC = . (iii) ∠BCA = . (iv) Line segment AC bisects and ____.

Solution From the figure, we observe that AB = AD and ∠BAC = ∠ DAC. Then (i) ∆ADC ≅ ∆ ABC. (ii) BC = DC. (iii)... View Article

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