Question

find the value of x and y when given a triangle whose midpoints are connecte
48
5x
3y°
y+3°
answer:
x =
y =

Explanation:

Step1: Apply Midsegment Theorem

The segment connecting midpoints of two sides of a triangle is half the length of the third side. So:
$$5x = \frac{1}{2} \times 48$$

Step2: Solve for x

Calculate the right-hand side and isolate x:
$$5x = 24 \implies x = \frac{24}{5} = 4.8$$

Step3: Use corresponding angles property

The midsegment creates a smaller similar triangle, so corresponding angles are equal:
$$3y = y + 3$$

Step4: Solve for y

Rearrange the equation to isolate y:
$$3y - y = 3 \implies 2y = 3 \implies y = \frac{3}{2} = 1.5$$

Answer:

$x = 4.8$
$y = 1.5$