L2 Algebra
Question Bank
The diagram below shows the design for a custom metal sign. The design starts with a 50 cm by 30 cm rectangular sheet of metal, and four identical squares are cut from the corners. The final area of the sign is 1400 cm². Find the side length, $x$, of the squares that were removed.
The right-angled triangle shown has an area of 21 cm². Calculate the value of x.
An open-top box is made from a thin sheet of metal. It has a square base. The height of the box is 5 cm more than the length of its base side. The total surface area of the box (the base and four sides) is 160 cm². Find the dimensions of the box.
The International Space Station (ISS) orbits at an altitude of 200 km above the Earth's surface. The total distance it travels in one complete orbit is 42,250 km. As shown in the diagram, the radius of the Earth is marked as $r$. Calculate the radius of the Earth.
A regular octagon is divded up by drawing lines from each vertex to the 'opposite' vertex, and a length is marked $d$, as shown in the diagram below.
Find an expression for the total area of the octagon in terms of $d$.
Both a square and a rectangle each have a perimeter of 44 cm. If their combined area is 238 cm², what are the dimensions of the rectangle?
An equilateral triangle has a base of $2x$. Find an expression for its area in terms of $x$.
The sides of an isosceles triangle are in the ratio 8 : 5 : 5. If the area of the triangle is 84 cm², what is the perimeter?
Four identical parallelograms make a pinwheel shape, as shown in the diagram. The area of the entire shape is 84 m². Find the perimeter of the shape.
The area of the right-angled trapezium shown below is 15 cm². Find the perimeter of the shape.
The perimeter of the semi-circle shown in the diagram is 30 m. The radius is labelled as y. Calculate the value of y giving your answer in terms of $\pi$.
The right-angled triangle and the square shown in the diagram have the same area. Calculate the value of x.
A right-angled triangle has side lengths in the ratio 3 : 4 : 5. If the area of the triangle is 216 cm², find the perimeter of the shape.
A rectangular photograph has a length that is twice its width. It is placed in a frame that creates a border of uniform width of 4 cm around the photo. The area of the border is equal to the area of the photograph. Find the dimensions of the photograph.
A rectangular garden bed is surrounded by a paved pathway of constant width. The garden bed has dimensions $(3n-4)$ metres by $(n+2)$ metres, while the outer edge of the pathway (including the garden bed) has dimensions $(3n+2)$ metres by $(n+8)$ metres. If the total area of the pathway is 156 m², find the width of the pathway.
The base of a rectangular container has a length of $(2h+3)$ cm and a width of $(h+1)$ cm. The length of the diagonal of the base is $d$ cm. Show that the height $h$ is given by the expression:
$h = \frac{-7 + \sqrt{5d^2 - 1}}{5}$
A hardware store is bundling 16 identical pipes for sale. The pipes are arranged in a 4x4 grid, and a metal band is wrapped tightly and securely around the outside of the bundle.
Each pipe has an inner radius of $r$ cm and a wall thickness of 2 cm. Find a expression for the total length of the metal band in terms of $r$ and $\pi$, give your answer in fully factorised form.