If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.
If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of the quadrilateral, find the area of the quadrilateral ABCD.
Find all zeroes of the polynomial (2x4 - 9x3 + 5x2 + 3x-1) if two of its zeroes are ( 2 + √3 ) and ( 2 - √3 ).
Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.
Given: Square ABCD with diagonal BD △ BCE which is described on base BC △ BDF which is described on base BD both △ BCE and △ BDF equilateral
To prove:
Proof:
Both △ BCE and △ BDF equilateral
In △ BDF and △ BCE
Hence by SSS similarity
△ FBD ~ △ BCE
We know that in similar triangles,
Ratio of area of a triangle is equal to the ratio of the square of the corresponding sides
But DB = √2 BC as DB is the diagonal of square ABCD
Hence,
Hence Proved
A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.