They both are complementary angles i.e their sum must equals 90°
4x+ 31 + 6x + 39 = 90
10x + 70 = 90
10x = 90-70
10x = 20
x = 2
we have to find angle ADC
just put the value of x in that expression for that angle.
angle ADC = 6x + 39 = 6 (2)+39 = 12 + 39 = 51°
Solve the equation for
t
t
by finding
a
a
,
b
b
, and
c
c
of the quadratic then applying the quadratic formula.
t
=
10
−
h
+
√
h
2
−
20
h
+
160
10
t
=
10
-
h
+
h
2
-
20
h
+
160
10
t
=
10
−
h
−
√
h
2
−
20
h
+
160
10
The area of the base is:
A = root ((s-a) * (s-b) * (s-c) * (s))
Where,
a, b, c: sides of the triangle
s = (a + b + c) / 2
We have then:
s = (9 + 9 + 9) / 2
s = 13.5
A = root ((13.5-9) * (13.5-9) * (13.5-9) * (13.5))
A = 35.07
Then, the surface area of the prism is:
S.A = 2 * A + 9h + 9h + 9h
Where,
h: height of the prism:
Substituting values:
421.2 = 2 * (35.07) + 9h + 9h + 9h
Clearing h:
27h = (421.2 - 2 * (35.07))
h = (421.2 - 2 * (35.07)) / (27)
h = 13
Answer:
the height of the box is:
h = 13 inches
