Question

A rectangle's base is 5 cm longer than its height. The rectangle's area is 50 cm². Find this rectangle's dimensions.

The rectangle's height is
The rectangle's base is

Answer 1

• The rectangle's height is 5 cm,
• The rectangle's base is 10 cm.

Explanation:

Let the dimensions be:

• Base = b, Height = h

Given

• b = h + 5,
• A = 50 cm²

The area of rectangle is:

• A = bh

• h(h + 5) = 50
• h² + 5h = 50
• h² + 5h - 50 = 0
• h² - 5h + 10h - 50 = 0
• h(h - 5) + 10(h - 5) = 0
• (h - 5)(h + 10) = 0

• h - 5 = 0 and h + 10 = 0
• h = 5 and h = - 10

The second value of h is negative and therefore discarded.

So we get:

• h = 5 cm,
• b = 5 + 5 = 10 cm