Question

if angle A is 90degree find x+y+z
​

Answer 1

Answer:

can you show the diagram?

Step-by-step explanation:

Answer 2

Step-by-step explanation:

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