CAT 2024 MOCK 1 – TRIANGLE

The sum of perimeters of an equilateral triangle and a rectangle is 90 cm. The area, T, of the triangle and the area , R, of the rectangle, both in sq cm, satisfy the relationship R = T². If the sides of the rectangle are in the ratio 1 : 3, then the length, in cm, of the longer side of the rectangle, is

From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is 's'. Then the area of the triangle is  

1.      S²/(2√3)
2.     2S²/(2√3)
3.     S²/√3
4.     √3 S²/2

In a triangle ABC , ∠ BCA =50°. D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then ∠ FDE, in degrees, is equal to   

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°. If BC = 10 inches then the area of the triangle in square inches is

In a triangle ABC, AB = AC = 8 cm. A circle is drawn with BC as diameter passes through A.  Another circle drawn with center at A passes through B and C.  Then the area, in sq.cm. of the overlapping region between the two circles is

Suppose the medians BD and CE of a triangle ABC intersect at a point O. If the area of triangle ABC is 108 sq. cm. , then the area of triangle EOD  in  sq. cm., is

In triangle  ABC , altitudes AD and BE are drawn to the corresponding bases . If  angle BAC  = 45˚  and angle ABC =  θ , then  AD / BE equals  

Let    ∆ ABC   be an isosceles triangle such that AB and AC are of equal length. AD is the altitude from A on BC and BE is the altitude from B on AC.  If AD and  BE intersect at 'O'  such that  angle AOB = 105 ˚, then  AD/ BE  equals

A triangle is drawn with its vertices on the circle C   such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b . If the radius of the circle is ‘r’ then  the are of the triangle is

  A.        abr² / 2 (a² + b²)

  B.         abr² / (a² + b²)²

  C.         4abr²/ (a² + b²)

  D.         2abr² / (a² + b²)

In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, is