In the figure angle Y is the right angle of triangle XYZ write the following ratios
Answers
A Square can be inscribed in a right triangle in 2 ways…..
(1) st : As shown above: Right triangle YXZ, < X= 90°, < Y = 45° ( given)
=> < Z = 45° => XY = XZ = a unit
So, YZ = √( a² + a²) = √2 a unit ………... (1)
Since , area of inscribed Square ABCD= 64 cm²
=> its each side = 8 cm
BC = 8cm ………….. (2)
In triangle BAY, < B = 90°, < Y = 45° So, third < BAY = 45°
=> BA = BY
=> BY = 8 cm ………….. (3)
Similarly in isosceles right triangle CZD
CD = CZ
= CZ = 8 cm …………… (4)
ZY = CZ + BC + BY
=> √2a = 8 + 8 + 8 = 24 ( by (1),(2),(3),& (4) )
=> a = 24/√2 = 12√2
& Area (triangle XYZ )= 1/2 * a * a
=> area = 1/2 * 12√2 * 12√2
=> area = 144
Area( tri XYZ) = 144 cm² . . . . . . . Ans
(2)nd: If square is inscribed in such a way that
1 vertex of the square is on the hypotenuse, 2 vertices of the square on each side of the triangle & 4th vertex is right angled vertex of the triangle…
In this case area of triangle XYZ = 1/2 * 16 * 16 =
128 cm² . . . . . . . . . Ans
Answer:
CZD IS A RIGHT ANSWER ISOSELES TRIANGLE