Question

a rectangle has a width that is 7 centimeters less than its length, and it’s area is 330 square centimeters. what are the dimensions of the rectangle?

Answer 1

Answer:

The dimensions of the rectangle are 22cm of length and 15cm of width

Step-by-step explanation:

To solve this we first have to know the formula to calculate the area of ​​a rectangle

a = area = 330 cm²

L = length  =

w = width = L - 7cm

a = l * w

we replace with the known values

330 cm² = L * (l - 7cm)

330 cm² = L² - 7Lcm

0 = L² - 7Lcm - 330 cm²

when we have an equation like this we can use bhaskara

a = 1

b = -7Lcm

c = -330cm²

ax² + bx + c = 0

x = -b(±)√(b² - 4ac)/2a

we replace with the known values

L = -(-7cm)(±)√(7² - 4(1)(-330cm²)) / 2(1)

L = 7cm(±)√(49 + 1320cm²)) / 2

L = 7cm(±)√(1369cm²)) / 2

L1 = (7cm + 37cm) / 2

L1 = 44cm / 2 = 22cm

L2 = (7cm - 37cm) / 2

L2 = -30cm / 2 = -15cm

The positive represents the unknown with which we work (L) and the negative with which we do not work (W)

The dimensions of the rectangle are 22cm of length and 15cm of width