Grades 7-8 Video Solutions 2024-2024_7-8

Video Transcription

Problem number three. The first diagram shows a rhombus. The area of the first diagram is  increased by adding two right triangles, as shown. By what percentage has the area increased?  So if we look at the diagram, we can notice that there is a lot of symmetry in the rhombus,  and in particular if we draw the two diagonals of the rhombus, we get a figure that looks like this.  Now if we notice that in this figure we have six triangles, two of which are the additional right triangles that we added. And we can also notice that by the symmetry of the figure,  all six of these triangles have equal area. So the increase that we added is these two gray triangles, and that was from the original four light gray triangles. So that means that  the percent increase would be six minus four, which is the number of added triangles, over  the initial number of triangles, which is four. And we multiply that by 100% to convert into a  percentage. Six minus four is two, so two over four times 100% equals 50%. And so that means that our answer is E, 50%.

Video Summary

The problem involves a rhombus whose area is increased by adding two right triangles. By analyzing the figure's symmetry, it's found that the rhombus, divided by its diagonals, forms six triangles of equal area—four originally and two added. The area increase is calculated using the formula \((\text{new area} - \text{original area})/\text{original area} \times 100\%\), resulting in \((6 - 4)/4 \times 100\%\), which equals a 50% increase. Therefore, the area of the rhombus increases by 50%, making the answer to the problem 50%.

Keywords

rhombus

area increase

right triangles

symmetry

percentage calculation