Question
If the scale factor of two similar triangles is a:b, then the ratio of their area is
- a2 : b2
- a : 2b
- a : b
- a3 : b3
Hint:
We know if triangles are similar then the ratio of their areas is equal to square of ratio of their sides.
Given ratio of sides =
The correct answer is: a2 : b2
We know if triangles are similar then the ratio of their areas is equal to square of ratio of their sides.
Given ratio of sides =
Area of a triangle is 
In similar triangles, the lengths of corresponding sides are in proportion.
Since scale factor is a:b, the ratio of corresponding sides is a : b
Now, ratio of areas of triangles will be 
= 
= 
Related Questions to study
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If the two triangles are similar. Find the value of angle L.
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1.) Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size
If the corresponding angles of two triangles are equal, then the triangles are similar. They are called equiangular triangles
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If the corresponding angles of two triangles are equal, then the triangles are similar. They are called equiangular triangles
Find the value of x in the following figure:
Find the value of x in the following figure:
In the given figures, ∆ABC ~ ∆DEF, then find the unknown value x.
In the given figures, ∆ABC ~ ∆DEF, then find the unknown value x.
The figures given below are
The figures given below are
If triangles ADE and ABC shown in the figure are similar, what is the value of x?
If triangles ADE and ABC shown in the figure are similar, what is the value of x?
In similar triangles, the angles are
In similar triangles, the angles are
When the ratio of corresponding sides is proportional, and angle are equal in two figures, then the figures are
When the ratio of corresponding sides is proportional, and angle are equal in two figures, then the figures are
If the scale factor is 
, the dilation is
Scale factor : Scale Factor is defined as the ratio of the size of the new image to the size of the old image
• If the scale factor is greater than 1, the image is an enlargement. It expands.
• If the scale factor is between 0 and 1, the image is a reduction. It contracts.
• If the scale factor is 1, the figure and the image are the exact same size (congruent).
If the scale factor is , the dilation is
Scale factor : Scale Factor is defined as the ratio of the size of the new image to the size of the old image
• If the scale factor is greater than 1, the image is an enlargement. It expands.
• If the scale factor is between 0 and 1, the image is a reduction. It contracts.
• If the scale factor is 1, the figure and the image are the exact same size (congruent).
Find the value of the variable m and n for the following figure that undergoes a dilation.
Scale factor : Scale Factor is defined as the ratio of the size of the new image to the size of the old image
• If the scale factor is greater than 1, the image is an enlargement. It expands.
• If the scale factor is between 0 and 1, the image is a reduction. It contracts.
• If the scale factor is 1, the figure and the image are the exact same size (congruent).
Find the value of the variable m and n for the following figure that undergoes a dilation.
Scale factor : Scale Factor is defined as the ratio of the size of the new image to the size of the old image
• If the scale factor is greater than 1, the image is an enlargement. It expands.
• If the scale factor is between 0 and 1, the image is a reduction. It contracts.
• If the scale factor is 1, the figure and the image are the exact same size (congruent).
