Question

semester b
what is the perimeter of rectangle jklm?
12
10
64 units
32 units
56 units
44 units

Explanation:

Step1: Analyze triangle JML

In rectangle JKLM, triangle JML is a right triangle with one leg \( JM = 12 \) and hypotenuse \( JL = 2\times10 = 20 \) (diagonals of a rectangle are equal and bisect each other). Let the other leg \( ML = x \). Using the Pythagorean theorem \( a^2 + b^2 = c^2 \), we have \( 12^2 + x^2 = 20^2 \).

Step2: Solve for ML

Calculate \( 12^2 = 144 \) and \( 20^2 = 400 \). Then \( x^2 = 400 - 144 = 256 \), so \( x = 16 \) (since length is positive).

Step3: Calculate perimeter of rectangle

The length and width of the rectangle are 16 and 12. The perimeter formula for a rectangle is \( P = 2(l + w) \). Substitute \( l = 16 \) and \( w = 12 \): \( P = 2(16 + 12) = 2\times28 = 56 \) units.

Answer:

56 units