Question
Statements : No triangle is a square. Some
squares are rectangles. All rectangles are circles. Conclusions : I. Some circles are rectangles. II. Some rectangles are not triangles. III. All squares being circle is a possibility. In each of the questions below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of given conclusions logically follows from the given statements disregarding commonly known facts.Solution
All rectangles are circles (A)⇒ Conversion ⇒ Some circles are rectangles (I). Hence, conclusion I follows. No triangle is a square(E) + Some squares are rectangles(I) ⇒ Some rectangles are not triangles(O*). Hence, conclusion II follows. Some squares are rectangles(I) + All rectangles are circles(A) ⇒ Some squares are circles(I) )⇒ Probable conclusion ⇒ All squares may be circles(A). Hence, conclusion III follows.
- A triangle has a base of 22 cm and the corresponding height is 9.5 cm. Calculate its area.
Calculate the hypotenuse of an isosceles right-angled triangle where the equal sides are 8√6 cm each.
What is the height of an equilateral triangle if each of its sides is 4√3 cm?
What is the height of an equilateral triangle if each side measures 8√3 cm?
In a ΔDEF, ∠D = 45°, ∠E = 2∠F. What is the value of ∠F?
If the ratio of the area of two similar triangles is √3:√2 then what is the ratio of the corresponding sides of the two triangles?
In a right-angled triangle, the legs are in the ratio 3:4, and the hypotenuse is 25 cm. Find the perimeter of the triangle.
If the side of an equilateral triangle is 12cm, then find the area (in cm 2 ) of the triangle (correct to two decimal places).
The corresponding medians of two similar triangles are 12 cm and 15 cm. If the area of the first triangle is 288 cm, then find the area of the second tr...
An equilateral triangle ABC is surmounted on a square BCDE whose area is 500 cm². Find the altitude of triangle ABC.