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The shorter leg of a right triangle is 6ft shorter than the longer leg. The hypotenuse is 6ft longer than the longer leg. Find the side leng
Question
The shorter leg of a right triangle is 6ft shorter than the longer leg. The hypotenuse is 6ft longer than the longer leg. Find the side lengths of the triangle.
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Mathematics
3 years
2021-09-05T13:45:39+00:00
2021-09-05T13:45:39+00:00 2 Answers
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Answers ( )
Answer:
mmm I think you first subtraction
Length of the longer side =
24
m
Length of the shorter side =
18
m
Length of the hypotenuse =
30
m
Explanation:
From the data given, we can write:
Length of the longer side =
x
Length of the shorter side =
x
−
6
Length of the hypotenuse =
x
+
6
The Pythagorean Theorem states the the square of the hypotenuse is equal to the sum of the squares of the other two sides. Hence.
x
2
+
(
x
−
6
)
2
=
(
x
+
6
)
2
x
2
+
x
2
−
12
x
+
36
=
x
2
+
12
x
+
36
Cancel equivalent terms on each side.
x
2
+
x
2
−
12
x
+
36
=
x
2
+
12
x
+
36
x
2
−
12
x
=
12
x
Subtract
12
x
from each side.
x
2
−
24
x
=
0
Factorise.
x
(
x
−
24
)
=
0
x
=
0
or
x
−
24
=
0
x
=
0
or
x
=
24
Since the length has to be a positive integer, the length of the longer side is
24
m
.
Hence:
Length of the longer side =
24
m
Length of the shorter side =
18
m
Length of the hypotenuse =
30
m
To verify, we apply the Pythagorean Theorem:
24
2
+
18
2
=
30
2
576
+
324
=
900
Since the two sides are equal, the calculations have been verified.