The hypotenuse of a right triangle
us 17 cm long from it the sumining
two sides is 8em in length, then
the length of the other side is :
please give full solution
Answers
the length of the other side is = √(17)^2 - (8)^2
= √ 289- 64 =√225 = 15cm
Answer:
Using the Pythagorean theorem we know that any right triangle with sides a, b and c the hypotenuse:
a
2
+
b
2
=
c
2
c
=
17
a
=
x
b
=
x
+
7
a
2
+
b
2
=
c
2
x
2
+
(
x
+
7
)
2
=
17
2
x
2
+
x
2
+
14
x
+
49
=
289
2
x
2
+
14
x
=
240
x
2
+
7
x
−
120
=
0
(
x
+
15
)
(
x
−
8
)
=
0
x
=
−
15
x
=
8
obviously the length of a side cannot be negative so the unknown sides are:
8
and
8
+
7
=
15
Step-by-step explanation:
let the third side Explanation:
let the third side
=
x
then the other side
=
x
+
7
←
7 cm longer
using
Pythagoras' theorem
square on the hypotenuse
=
sum of squares of other sides
(
x
+
7
)
2
+
x
2
=
17
2
x
2
+
14
x
+
49
+
x
2
=
289
2
x
2
+
14
x
−
240
=
0
←
in standard form
divide through by 2
x
2
+
7
x
−
120
=
0
the factors of - 120 which sum to + 7 are + 15 and - 8
(
x
+
15
)
(
x
−
8
)
=
0
equate each factor to zero and solve for x
x
+
15
=
0
⇒
x
=
−
15
x
−
8
=
0
⇒
x
=
8
x
>
0
⇒
x
=
8
lengths of unknown sides are
x
=
8
and
x
+
7
=
8
+
7
=
15
=
x
then the other side
=
x
+
7
←
7 cm longer
using
Pythagoras' theorem
square on the hypotenuse
=
sum of squares of other sides
(
x
+
7
)
2
+
x
2
=
17
2
x
2
+
14
x
+
49
+
x
2
=
289
2
x
2
+
14
x
−
240
=
0
←
in standard form
divide through by 2
x
2
+
7
x
−
120
=
0
the factors of - 120 which sum to + 7 are + 15 and - 8
(
x
+
15
)
(
x
−
8
)
=
0
equate each factor to zero and solve for x
x
+
15
=
0
⇒
x
=
−
15
x
−
8
=
0
⇒
x
=
8
x
>