Verified answer

QUADRATIC EQUATIONS IN REAL LIFE

Problem:

The area of a rectangular pathway is 350 sq. meters and its perimeter is 90 m.What is the sum of the roots of quadratic equation?

A. 45

B. 44

C. 90

D. 80

Answer with Step-by-step explanation:

To determine the sum of the roots of the quadratic equation, we can make two linear equations with two unknowns.

Let: L = length of the rectangle

W = width of the rectangle

Recall that the area of the rectangle can be obtain by multiplying its length and width so:

A = L x W

350 = L x W

Let this equation be Equation #1.

For the perimeter, we have to get twice the sum of the dimensions.

P = 2 (L + W)

90 = 2 (L + W)

Divide both sides by 2.

90/2 = 2(L+W)/2

45 = L + W

L = 45 - W

Let this equation be Equation #2.

Substitute Equation #2 to the value of L in Equation #1:

350 = (45 - W) x W

350 = 45W - W²

W² - 45W + 350 = 0

By factoring:

(W - 35)(W - 10) = 0

W1 = 35 and W2 = 10

The length should be shorter than the width so we need to take 10 as the width.

Going back to Equation #1:

350 = L x w

350 = 10L

350/10 = 10L/10

L = 35

Therefore, the dimensions of the rectangular pathway is 35 meters by 10 meters.

On the other hand, the sum of the roots of the quadratic equation is 45.

The correct answer is letter A.

Read more about real-life applications of quadratic equations:

brainly.ph/question/4679508

#BRAINLYFAST