The perimeter of a rectangular playfield is 28\text{ m} and its area is 40\text{ m}^2. Wha… — JAMB UTME

The perimeter of a rectangular playfield is $28\text{ m}$ and its area is $40\text{ m}^2$ . What is the positive difference, in metres, between its length and width?

Cevap: 6 m

Cevap

The positive difference between the length and width of the playfield is 6 metres.

Formulating the system gives

x + y = 14

and

xy = 40

. Substituting

y = 14 - x

yields the quadratic equation

x^2 - 14x + 40 = 0

, which factors into

(x - 10)(x - 4) = 0

. The dimensions are

10\text{ m}

and

4\text{ m}

, giving a positive difference of

10 - 4 = 6\text{ m}

Adım Adım Çözüm

Set up linear and quadratic equations for perimeter and area

x + y = 14

and

xy = 40

Perimeter formula is

2(x + y) = 28

which simplifies to

x + y = 14

, and area formula is

xy = 40

Substitute

y = 14 - x

into the quadratic area equation

x(14 - x) = 40 \implies x^2 - 14x + 40 = 0

Substitution reduces the simultaneous system to a single quadratic equation in terms of

x

Solve the quadratic equation by factoring

(x - 10)(x - 4) = 0 \implies x = 10 \text{ or } x = 4

The roots of the equation give the dimensions of the rectangle.

Calculate the positive difference between the two dimensions

10 - 4 = 6

Subtract the smaller dimension from the larger dimension.

Anahtar Kavram

Solving word problems involving simultaneous linear and quadratic equations

Tahmini Süre:1m 30s

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