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.

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.

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step-by-step explanation:

answer: the first graph

step-by-step explanation: