Question

A rectangle has length x and width x-3. The area of

the rectangle is 10 square meters.
Mark this and return
X
10 m²
X-3
Complete the work to find the dimensions of the
rectangle.
x(x-3) = 10
x²-3x = 10
x²-3x-10-10-10
(x+2)(x-5)=0
What are the width and length of the rectangle?
4
O The width is 1 meter and the length is 10 meters.
O The width is 10 meters and the length is 1 meter.
O The width is 2 meters and the length is 5 meters.
O The width is 5 meters and the length is 2 meters.
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Answer 1

The width is 2 meters and the length is 5 meters.

Answer 2

the width is 2m and the length is 5m

Explanation:

the area (A) of a rectangle is calculated as

A = length × width

= x(x - 3)

given A = 10 , then

x(x - 3) = 10

x² - 3x = 10 ( subtract 10 from both sides )

x² - 3x - 10 = 0 ← in standard form

(x - 5)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 2 = 0 ⇒ x = - 2

however, x > 0 , then x = 5 and x - 3 = 5 - 3 = 2 , so

the width is 2m and the length is 5m