Question

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

The perimeter of the rectangle is 34 cm. The perimeter of the triangle is 30 cm. Find the value of n.

Please select the best answer from the choices provided

A. 10cm
B. 14cm
C. 12cm
D. 16cm

Answer 1

12 cm. Just took the quiz! 12 is the right answer not 14 cm.

Explanation:

Answer 2

9514 1404 393

Answer:

C. 12cm

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

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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.