The dimensions of the triangle shown are to be enlarged using a scale factor of 2.
Find the enlarged length of:
The dimensions of the triangle shown are to be reduced using a scale factor of \dfrac{1}{2}.
Find the reduced length of:
The dimensions of the triangle shown are enlarged using a scale factor of 3.1.
Find the new length of:
The dimensions of the triangle shown are reduced using a scale factor of 0.92
Find the new length of:
For the given similar figures, find the scale factor from the larger figure to the smaller figure:
Consider the following quadrilaterals:
Is quadrilateral A'B'C'D' an enlargement of quadrilateral ABCD?
Find the scale factor
For the given similar figures, the scale factor used to enlarge the smaller quadrilateral is 2. Find the length of FG.
The scale factor of these similar triangles is 4:5. Find:
The reduction factor
The enlargement factor
The scale factor of these similar figures is 14:5. Find:
The reduction factor
The enlargement factor
The ratio of the lengths of the corresponding sides in these similar figures is 1:4.
Find the scale factor from the smaller figure to the larger figure.
Triangle ABC has been reduced to form a smaller triangle A'B'C'. Find the scale factor.
Triangle ABC has been enlarged to triangle A'B'C'. Find the scale factor.
For the similar figures given, the scale factor used to enlarge the smaller quadrilateral is 4.5. Find the length of FG.
If an image is enlarged by 250\%, what will be the scale factor?
The two figures shown are similar. \triangle PQR is a reduction of \triangle ABC.
Find the scale factor applied to \triangle ABC to get \triangle PQR.
Hence, find the length of PR.
The two figures below are similar:
Find the reduction factor
Hence find the value of a
The two quadrilaterals in the diagram are similar. Find the value of y.
The two quadrilaterals in the diagram are similar. Find the value of b.
In the cartesian plane shown, is the larger triangle a dilation of the smaller triangle?
In the cartesian plane shown, is the smaller triangle a dilation of the larger triangle?
In the cartesian plane shown, is the smaller quadrilateral a dilation of the larger quadrilateral?
An equilateral triangle of side length 6 cm is to be enlarged by a factor of 5.
What will be the side length of the resulting triangle?
What will be the size of each angle in the resulting triangle?
Glass in the shape of a circle has a radius of 12 centimetres. When the glass is blown, the radius becomes 48 centimetres. Find the enlargement factor.
A circular oil spill has a radius of 20 metres. In a photo taken of the oil spill, the circle is reduced by a factor of 500. Find the radius of the circular oil spill in the photo, to the nearest centimetre.
A rectangle is 8 cm long and 6 cm wide. If its dimensions are enlarged such that the length is now 28 cm, find the new width.
Mae wants to insert a picture into a document. She enlarges it by a factor of 12 but it becomes too blurry, so she reduces the resulting picture by a scale factor of 4. Find the overall scale factor from the original to the final size.
A 1.1 m high fence casts a shadow of length 1.5 m. At the same time, a lamp post of height 3.9 metres casts a shadow of length L metres. Find the value of L, rounding to one decimal place.
Council has designed plans for a triangular courtyard in the town square. Their drawing shows the courtyard to have dimensions of 4 cm, 6 cm and 9 cm. The shortest side of the actual courtyard is to be 80 metres long.
State the longest side length of the actual courtyard in metres.
State the middle side length of the actual courtyard in metres.
A boy wants to measure his height. He stands in the sun and takes note of where his shadow ends and places a 76 cm pole vertically in the ground at the end of his shadow. He then measures the height and length of the stick's shadow.
Find the height of the boy.
A 5.6 m ladder has a strut 190 cm long placed 2.3 m from the top.
If the feet of the ladder are d m apart, find the value of d. Round your answer to two decimal places.
Sharon wants to measure the height of a flagpole. She places a mirror facing up on the ground between herself and the flagpole such that the mirror is 7.2 metres from the flagpole's base. She then backs away until a reflection of the top of the flagpole appears in the mirror.
If she stops moving backwards at a point that is 2.5 metres from the mirror and if her eye level is 1.54 metres above the ground, find the height of the flagpole in metres.
A large tree casts a shadow of 32 m. At the same time, a 1.2 m high fence post, standing vertically, casts a shadow of 4.5 m. Find h, the height of the tree in metres.
A 4.9 m high flagpole casts a shadow of 4.5 m. At the same time, the shadow of a nearby building falls at the same point S. The shadow cast by the building measures 13.5 m. Find h, the height of the building, using a proportion statement.
Two similar triangles are created by cables supporting a yacht's mast.
Find the height of the mast.
A surveyor needs to measure the distance across a river at a place where the banks are straight and parallel. There are two trees on the opposite bank that are 37 m apart. She stands 8 m from the bank, directly opposite the first tree. Her assistant has to move 7.7 m along the bank to place a stick directly in her line of sight to the second tree.
Find the distance, d, across the river. Round your answer to two decimal places.
In the diagram \triangle ABD and \triangle ECD are similar right-angled triangles, with \\ AE = 10, \text{ } AB = 6 and EC = 1.2.
Let x be the length of interval ED. Find the exact length of x.
Hence find the radius of the circle. Round your answer to one decimal place.
Engineers want to determine the distance for a bridge to be built between points A and B. The diagram is an aerial view of their measurements. Point C is chosen so that AC is perpendicular to AB. DE is parrallel to AB.
The following measurements are taken:
- CA = 300\text{ m}
- CD = 140\text{ m}
- DE = 150\text{ m}
Calculate the distance AB, to the nearest metre.
