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2 years ago

A rectangle with length n and height m. A right triangle with hypotenuse n + 1, length n, and height m.

Mathematics

1 answer:

Oksana_A [137]2 years ago

8 0

9514 1404 393

Answer:

C. 12cm

Step-by-step explanation:

The equation for the perimeter of the rectangle is ...

P = 2(L+W)

34 = 2(n +m)

Solving for m, we get

m = 17 -n . . . . . . . divide by 2, subtract n

The Pythagorean theorem gives the relationship between the sides and the hypotenuse

m^2 +n^2 = (n+1)^2

(17 -n)^2 +n^2 = (n +1)^2 . . . . . . substitute for m

289 -34n +n^2 +n^2 = n^2 +2n +1 . . . . eliminate parentheses

n^2 -36n +288 = 0 . . . . . . . put in standard form

(n -12)(n -24) = 0 . . . . . . . . . factor

n = 12 . . . . . . . . . . n=24 is an extraneous solution here

The value of n is 12 cm.

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Explanation:

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Step-by-step explanation:

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