Could someone please explain how to solve these questions in geometry? Preferably step by step please. Thanks!

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Could someone please explain how to solve these questions in geometry? Preferably step by step please. Thanks!

Mathematics
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I shall attach the file, wait.
the area of triangle abc = 1/2 X BC * height of the triangle = 48 (BC/2) X h = 48 h = 96/BC also by pythagoras 10^2 = (0.5BC)^2 + h^2 plug h into this last equn: 100 = 0.25BC^2 +(96/BC)^2) this reduces to 100x^2 = 0.25x^4 + 9216 let x^2 = X 100X = 0.25X^2 + 9216 Soling this gives X = 144 or 256 ie x = 12 or Answer BC = 16

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triangles xvz and yxz are congruent (same shape and same size) so xv = xy = 5 and yz = vz = 1. now we can form two simultaneous triangles . let vw = x and wz = y consider triangle wvz, by pythagoras: y^2 = x^2 + 1^2..........................(1) now consider triangle, by pythagoras: (5+x)^2 = (x+1)^2 + 25................(2) Solve (1) and (2) to get values of x and y x = length of vw
next question area of semicircle = 1/2 * pi* 3^2 = 4.5pi area of triangle = 1/2 * CA * height CA = 6 and height = 5-3 = 2 so area of triangle = 3 * 2 = 6 Area of the whole figure is 4.5pi + 6
the answer to second question is vw = 5/12
for the 2nd number, what makes the 2 triangles congruent? aren't they just similar? for the 3rd number, what do you mean by CA? Thanks!

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