Quadratic Equation Area Problems

The side length of a square is 𝑥, and the dimensions of a rectangle are 𝑥 and 2. Given that the sum of the two areas is 15, determine the perimeter of the square.

The yellow area is 21.

Which of the following equations is correct?

• 2x²+x-21=0

• 2x²-x-21=0,

• 2x²-x+21=0,

• 2x²+x+21=0,

The correct equation was 2x²+x-21=0.

Factorise 2x²+x-21

• (x+7)(x-3)

• (x-3)(x+3)

• (2x+7)(x-3)

• (2x-7)(x+3)

• (2x-7)(x-3)

The correct equation was 2x²+x-21=0.

This factorises to (2x+7)(x-3)=0

Enter the correct value of x

Tags

CCSS.HSA-REI.B.4B

The diagram shows the floor plan of a building.

The total area is 24.

This leads to the equation x²+x-a=0

Find the value of a

The diagram shows the floor plan of a building.

The total area is 24.

This leads to the equation x²+x-6=0

Find the value of x

Given that the area is 22, which is the correct equation?

• x²+7x-44=0

• x²-7x+44=0

• x²+9x-22=0

• x²-9x+22=0

If the area is 22, we can form the equation

x²+7x-44=0

Find x.

Tags

CCSS.6.G.A.1

Find x

Tags

CCSS.6.G.A.1

A rectangular photograph measuring 6 cm by 4 cm is to be displayed in a card mount in a rectangular frame, as shown in the diagram.

Which of the following equations can be used to find 𝑥 if the area of the mount is 64 cm²?

• (4+2𝑥)(6+2𝑥)−24=64

• (3+2𝑥)(6−5𝑥)−21=32

• (7+2𝑥)(5+2𝑥)−13=64

• (9+5𝑥)(3+7𝑥)−15=18

• (5+2𝑥)(7−2𝑥)−24=28