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The area of the isosceles triangle is 5/4 √11cm², if the perimeter is 11 cm and the base is 5 cm. Write True or False and justify your answer.

The given statement is True Explanation Area of triangle = √s(s-a)(s-b)(s-c) Perimeter = 11cm And base, a = 5 As the triangle is... View Article

The area of △ ABC is 8 cm² in which AB = AC = 4 cm and ∠A = 90º. Write True or False and justify your answer.

The given statement is True Explanation Area of triangle = × Base × Altitude Given that base= 4 cm height =6 cm =... View Article

The area of a triangle with base 4 cm and height 6 cm is 24 cm². Write True or False and justify your answer.

The given statement is False Explanation Area of triangle = × Base × Altitude Given that base= 4 cm height =6 cm =... View Article

The area of an equilateral triangle with side 2√3 cm is (A) 5.196 cm² (B) 0.866 cm² (C) 3.496 cm² (D) 1.732 cm²

The correct answer is (A) 5.196 cm2 An equilateral triangle has all three sides equal to each other. Due to this all the internal angles are of... View Article

The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is (A) 1322 cm² (B) 1311 cm² (C) 1344 cm² (D) 1392 cm²

The correct answer is (C) 1344 cm2 Explanation We know that Area of triangle = √s(s-a)(s-b)(s-c) According to the given details... View Article

The perimeter of an equilateral triangle is 60 m. The area is (A) 10√3 m² (B) 15√3 m² (C) 20√3 m² (D) 100√3 m²

The correct answer is (D) 100√3 m2 Explanation We know that area of an equilateral triangle of side a = √3/4 a2 According to... View Article

An isosceles right triangle has area 8 cm². The length of its hypotenuse is (A) √32 cm (B) √16 cm (C) √48 cm (D) √24 cm

The correct answer is (A) √32 cm Explanation Let us assume height of triangle to be = h Given that the triangle is isosceles, Let... View Article

Construct each of the following and give justification: A triangle PQR given that QR = 3cm, ∠ PQR = 45° and QP – PR = 2 cm.

Solution According to the given details We have to construct a triangle PQR such that QR = 3cm, ∠ PQR = 45° and QP – PR... View Article

Construct each of the following and give justification: A triangle if its perimeter is 10.4 cm and two angles are 45° and 120°.

Solution According to the given details We have to construct a triangle if its perimeter is 10.4 cm and two angles are 45° and... View Article

Construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.

Solution According to the given details We have to construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. And to bisect the... View Article

Draw an angle of 80° with the help of a protractor. Then construct angles of (i) 40° (ii)160° (iii) 120°.

Solution According to the given details We have to draw an angle of 80° with the help of a protractor. Then construct angles of (i)... View Article

Draw a line segment AB of 4 cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?

Solution According to the given details A line segment AB of length 4cm. To draw a perpendicular to AB through A and B, respectively. The... View Article

Draw an angle of 110° with the help of a protractor and bisect it. Measure each angle.

Solution According to the given details An angle ABC = 110o and to draw the bisector of ∠ABC The steps of construction for an... View Article

A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm. Write True or False in each of the following. Give reasons for your answer.

The given statement is True Explanation We know that the Sum of any two sides of a triangle must be greater than the third side. So as per the... View Article

An angle of 42.5° can be constructed. Write True or False in each of the following. Give reasons for your answer.

The given statement is False Explanation We know that, 42.5° = 1/2 x 85° An angle of 85° cannot be constructed with... View Article

An angle of 52.5° can be constructed. Write True or False in each of the following. Give reasons for your answer.

The given statement is True Explanation An angle of 52.5°can be constructed by bisecting angle 105° 52.5° = ½... View Article

With the help of a ruler and a compass it is not possible to construct an angle of : (A) 37.5° (B) 40° (C) 22.5° (D) 67.5°

The correct answer is (B) 40° Solution With the help of a ruler and a compass, we can construct the angels, 90°, 60°, 45°,... View Article

Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

Given According to the given details Triangle ABC and l is the perpendicular bisector of BC. To Prove Angles bisector of ∠A and... View Article

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

Given ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. To Prove P, Q, C and D are... View Article

If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.

Given According to the given details P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the... View Article

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