QR is parallel to ST and PQ:QR = 2:1. Given the area of triangle PST is 18cm2, the area of triangle PQR in sq cm is?
Is ST a line in the interior of PQR?
If so, I must be missing something. Just knowing the ratio of two sides of PQR tells me nothing about the areas of either triangle.
Better explain the overall figure, not just a couple of lines.
PQR is an interior triangle within triangle PST. QR runs parallel to ST.
To find the area of triangle PQR, we need to know the lengths of its base and height. However, we only know the ratio of PQ to QR, which means we need some additional information.
If we assume that the heights of triangles PST and PQR are equal, we can proceed to solve the problem. Let's denote the height of triangle PST as h.
Since QR is parallel to ST and PQ:QR = 2:1, we can conclude that PQ:ST = 2:3.
Now, let's find the lengths of PQ and ST. We know that PQ:QR = 2:1, so if we denote the length of QR as x, then the length of PQ would be 2x. Similarly, since PQ:ST = 2:3, the length of ST would be (2x/2)*3 = 3x.
Now, we have the lengths of PQ and ST in terms of x, and we know the area of triangle PST is 18 cm^2. The formula for the area of a triangle is given by A = (base * height) / 2.
Substituting the values:
18 = (3x * h) / 2.
To find the value of h, we can rearrange the equation:
h = (18 * 2) / (3x) = 12 / x.
Now, we can substitute the value of h into the formula to find the area of triangle PQR, which would be (2x * h) / 2 = xh.
Substituting the value of h:
Area of triangle PQR = x * (12 / x) = 12 cm^2.
Therefore, the area of triangle PQR is 12 square centimeters.