Question

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

Answer 1

I shall attach the file, wait.

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

the answer to second question is vw = 5/12

Answer 6

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!