Answer
Part a: 32.5 cm
Part b: 1 cm : 2.5 cm
Work Step by Step
Part a: Using proportions will make this problem easier to visualize:
$\frac{\text{base of the original triangle}}{\text{base of the enlarged triangle}}$=$\frac{\text{height of the original triangle}}{\text{height of the enlarged triangle}}$
Substitute the given values into the proportion:
$\frac{\text{13}}{x}$=$\frac{\text{7}}{\text{17.5}}$
Cross Products Property (AKA cross multiply and divide):
13(17.5)=7$x$
Simplify by multiplying the left side of the equation and then dividing 7 on each side:
$\frac{\text{227.5}}{7}$=32.5
The base of the enlarged triangle is 32.5 cm
Part b: The scale in this problem would be found by using a ratio of two corresponding sides of the triangles. For example, to get from the height
of the original triangle to the height of the enlarged triangle, write out the equation 7$x$=17.5 (7 times what number will give us 17.5)
Divide 7 on both sides of the equation so that $x$=2.5
Also, you can use the bases to determine the scale. To get from the base of the original triangle to the base of the enlarged triangle, write out the equation 13$x$=32.5 (13 times what number will give us 32.5)
Divide 13 on both sides of the equation so that $x$=2.5
The scale of the model is 1 cm : 2.5 cm. For every 1 cm on the original triangle, it is 2.5 cm on the enlarged triangle.
