Given that the two triangles are similar, the ratio of their corresponding sides is equal. Let's denote the height of the larger triangle as h.
Using the ratio of corresponding sides,
x/30 = y/135
We also know that the area of a triangle is given by (base * height) / 2. For the smaller triangle:
(30 * h) / 2 = 45
15h = 45
h = 3 cm
Now, we can solve for x and y using the relationships:
x/30 = 3/135 (since x is the height of the smaller triangle and 30 is one of its bases)
x/30 = 1/45
x = 30/45
x = 2/3
x = 0.67 cm
y/135 = 3/135 (since y is the height of the larger triangle and 135 is one of its bases)
y/135 = 1/45
y = 135/45
y = 3 cm
Therefore, the values of x and y are:
x = 0.67 cm
y = 3 cm.
The two triangles given are similar. Find the values of x and y when the smaller triangle has an area of 45 cm squared.
x
y
135 cm
30 cm
1 answer