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There is a rectangle with a perimeter of 90 meters, and an area of 464 square meters. What is the Dimensions of the rectangle?

Sagot :

rspill6

Answer: W = 29 and L = 16

Step-by-step explanation:

Perimeter, P, of a rectangle is 2L+2W (L and W are length and width)

Area, A, of a rectangle is L*W

We know:

P = 90 meters

A = 464 meters^2

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90 meters = 2L+2W

464 meters^2 = L*W

Rearrange the second equation:

L = (464 meters^2)/W

Use this value of L in the first equation:

90 meters = 2L+2W

90 meters = 2*((464 meters^2)/W)+2W

90 meters = ((928 meters^2)/W)+2W

90 meters = ((928 meters^2)/W)+2W

90*W meters = (928 meters^2)+2W^2 Multiply both sides by W

2W^2 -90W + 928 m^2 = 0

W^2 -45W + 464 m^2 = 0 [Divide both sides by 2]

Use the quadratic equation or factor the expression:

(x-16) and (x-29) , The solutions are 29 and 16, each in meters.

[(x-16)*(x-29)= x^2 -45x + 464

W = 29 and L = 16

P = 2*(29)+2(16) This is equal to 90 meters Checks.

A = 29*16 = 464 m^2 Checks

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