A rectangle on a coordinate plane has a length of 5 units and a width of 3 units. If the rectangle is dilated by a scale factor of 5, what is its new area?
I apologize for that. Let me simplify the explanation for you.
The original rectangle has a length of 5 units and a width of 3 units.
When we dilate the rectangle by a scale factor of 5, we multiply the length and width of the rectangle by 5 to get the new dimensions.
So, the new length is 5 multiplied by 5 which is 25 units, and the new width is 3 multiplied by 5 which is 15 units.
To find the new area of the dilated rectangle, we multiply the new length (25 units) by the new width (15 units).
So, the new area is 25 multiplied by 15, which equals 375 square units.
Therefore, the new area of the dilated rectangle is 375 square units.
Let $x$ be the scale factor of the dilation. If the area of the dilated triangle is $6.25$ times as great as the original figure, then the area of the dilated triangle is $6.25$ times the area of the original triangle.
Let $A$ be the area of the original triangle. The area of the dilated triangle is $Ax^2$, since the area of a figure is proportional to the square of the scale factor. Therefore, we have the equation $Ax^2 = 6.25A$.
Dividing both sides of the equation by $A$, we get $x^2 = 6.25$. Taking the square root of both sides, we have $x = \sqrt{6.25} = \boxed{2.5}$.
Therefore, the scale factor of the dilation is 2.5.
The new length of the rectangle is $5(5)=25$ units and the new width is $3(5)=15$ units. The new area is $(25)(15)=\boxed{375}$ square units.
I cant read that
A triangle on a coordinate plane was dilated. After being dilated, its area is 6.25 times as great as the original figure. What was the scale factor
Use proportions to find the missing side length (x) in the two similar figures.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A9.99 yards%0D%0A9.99 yards%0D%0A%0D%0A1.05 yards%0D%0A1.05 yards%0D%0A%0D%0A4 yards %0D%0A4 yards %0D%0A%0D%0A16.92 yards
To find the missing side length $x$ in the two similar figures, we can set up a proportion based on the corresponding sides of the figures.
Let's represent the corresponding sides in the first and second figures as $a$ and $b$, respectively. Then we can set up the proportion $\frac{a}{b}=\frac{x}{4}$.
Cross-multiplying, we have $a\cdot 4 = b\cdot x$.
Since the figures are similar, the ratio of corresponding side lengths will be the same. This means that $a:b$ is the same ratio as $9.99:16.92$.
Setting up the proportion $\frac{9.99}{16.92}=\frac{x}{4}$, we can cross-multiply to solve for $x$.
This gives us $9.99\cdot 4 = 16.92 \cdot x$.
Simplifying, we have $x = \frac{9.99\cdot 4}{16.92}$. Evaluating this expression gives $x \approx \boxed{2.35}$ yards.
I can't read that.
Apologies for the formatting issue. Let's try to simplify the explanation.
To find the missing side length $x$ in the two similar figures, we can set up a proportion based on the corresponding sides of the figures.
Let's denote the length of the corresponding side in the first figure as $a$, and the corresponding side in the second figure as $b$. We can set up the proportion $\frac{a}{b}=\frac{x}{4}$.
Cross-multiplying gives us $a\cdot 4 = b\cdot x$.
Since the figures are similar, the ratio of corresponding side lengths will be the same. This means that the ratio of $a$ to $b$ is equal to the ratio of $9.99$ to $16.92$.
Setting up the proportion $\frac{9.99}{16.92}=\frac{x}{4}$, we can cross-multiply to solve for $x$.
This gives us $9.99\cdot 4 = 16.92 \cdot x$.
Simplifying, we have $x = \frac{9.99\cdot 4}{16.92}$. Evaluating this expression gives us $x \approx \boxed{2.35}$ yards.
Therefore, the missing side length $x$ in the two similar figures is approximately $2.35$ yards.