MATH SOLVE

3 months ago

Q:
# A rectangular price tag has an area of 36 square centimeters. Its perimeter is 26 centimeters. What are the dimensions of the price tag?

Accepted Solution

A:

Answer:4 cm by 9 cmStep-by-step explanation:The formula for area of a rectangle is A = LW, where L and W are the dimensions of the rectangle. We have 36 = LWThe formula for perimeter of a rectangle is P = 2L + 2W. We have26 = 2L + 2WSolve the area formula for any variable..36/L = WPlug that into the perimeter equation..26 = 2L + 2(36/L)Now simplify...26 = 2L + 72/LMultiply all 3 terms by L to get rid of the fraction...26L = 2L² + 72Now this is a quadratic equation, get all terms to one side and solve...2L² - 26L + 72 = 0Divide both sides by 2L² - 13L + 36 = 0Factor the left side(L - 9)(L - 4) = 0So L = 4, or 9If L = 4, then W = 36/4 = 9If L = 9. then W = 36/9 = 4either way, the dimensions are 4 cm by 9 cm