Let x stand for the number of meters of the longer leg.

Longer leg . . . . . . . . .x <-- longer leg

8 m more than that . . x + 8 <-- hypotenuse

shorter leg. . . . . . . . . . . 20 <-- shorter leg

According to the Pythagorean Theorem:

a² + b² = c²

(one leg)² + (other leg)² = (hypotenuse)²

(. . x . . .)² + ( . . 20 . . )² = (. . x + 8 . . . )²

Solve for x, already defined as the length of the longer leg

x² + 20² = (x + 8)²

1) Expand the binomial

x² + 20² = x² + 16x + 64

2) Subtract x² from both sides

20² = 16x + 64

- same as -

400 = 16x + 64

3) Subtract 64 from both sides to isolate the 16x term

336 = 16x

4) Divide both sides by 16 to isolate x, already defined as the length of the longer leg

21 = x <-- answer

Answer:

The longer leg is 21 m long

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Check:

The hypotenuse must be 29 m long.

(8 m longer than the longer leg)

21² + 20²   should equal  29²

441 + 400 should equal 841

      841      does equal   841

Check  ✓

h = l+8

s = 20

L = h-8

s^2 + l^2 = h^2

20^2 + (L)^2 = (L+8)^2

-L^2+(L^2+16L+64) = 20^2

16L+64=20^2

16L=336

L=21

L (longest leg) is 21.