TRIANGLES - 1 (Basic Properties) || Quantitative Aptitude || CAT 2021 || 05 October

In ΔABC, D and E are points on the sides AB and AC respectively, such that DE||BC. If AD = 4 cm, DB = 11 cm, AE = 7 cm and BC = 15.6 cm, then the sum of the lengths of DE and EC (in cm) is:

The sides of a triangle are in the ratio 4 : 3 : 2. If the perimeter of the triangle is 63 cm, then what will be the length of the largest side?

In the diagram, M is the midpoint of YZ, ∠XMZ = 32°, and ∠XYZ = 16°. The measure of ∠XZY is:

The area of an equilateral triangle is half the area of a square. The ratio of the side  of the said triangle and an edge of the square is:

The area of ΔPQR is 8 cm² and area of ΔABC is 18 cm² and BC = 5 cm. If ΔPQR ~ ΔABC, then the length of QR is:

The corners of an equilateral triangle ABC whose side is 15 cm are cut to form a regular hexagon PQRSTU. Then, what is the length of side of the hexagon?

In a ∆ABC, 2∠ABC = 9∠ACB and 2∠BAC = 7∠ACB. If AB = 8 cm, AC = 17 cm, then the length of BC is 

In Δ PQR, S and T are mid-points of PQ and PR, respectively. If ∠QPR = 75° and ∠PRQ = 40°, then ∠TSQ is:

In an isosceles triangle ABC with AB = AC and AD is perpendicular to BC, if AD = 6 cm and the perimeter of ∆ABC is 36 cm, then the area of ∆ABC is:

Find the area of an equilateral triangle whose side is 12 cm.