Forming Equations from Shapes Flashcards

All 6 cards in this deck

What equation do you form when you are told the perimeter of a rectangle?
e.g. width $w$, length 7 cm longer, perimeter 70 cm

$2w+2(w+7)=70$
Add all four sides and set the total equal to the perimeter.

A pair of opposite sides of a rectangle is labelled with two different expressions. What equation can you form?
e.g. the sides are labelled $5x-9$ and $2x+6$

Equate the opposite sides: $5x-9=2x+6$
Opposite sides of a rectangle are equal in length.

What are the steps to form and solve an equation from the perimeter of a shape?
e.g. a triangle with sides $x$, $x+2$ and $x+4$ cm has perimeter 18 cm

1. Add the sides: $x+(x+2)+(x+4)=3x+6$
2. Set equal to the perimeter: $3x+6=18$
3. Solve and give units: $x=4$ cm

True or false? The area of a rectangle with sides $2x$ and $(x+3)$ is $2x+2(x+3)$.

False.
That is the perimeter; the area is the product $2x(x+3)$.

What equation do you form when told two shapes have areas related to each other?
e.g. square A has side $x$, square B has side $(x+4)$, and B's area is 70 cm² greater

Write an expression for each area and link them as stated: $(x+4)^2=x^2+70$

What are the steps when an area condition gives a quadratic equation?
e.g. a rectangle measures $x$ by $(x+3)$ cm and has area 10 cm²

1. Form the equation: $x(x+3)=10$
2. Rearrange to $ax^2+bx+c=0$: $x^2+3x-10=0$
3. Factorise and choose the valid root: $(x+5)(x-2)=0$, so $x=2$ cm ($-5$ rejected)