Question

В треугольнике МРК, ∠M= 45 градусов , а высота РН делит сторону МК на отрезки МН и НК, соответственно равные 12 см и 18 см. Найдите площадь треугольника МРК. Выполнить рисунок по условию задачи

Answer 1

думаю что понятно написала

Answer 2

Problem Analysis

We are given a triangle MRC, where angle M is 45 degrees. The height RN divides the side MK into segments MN and NK, which are 12 cm and 18 cm respectively. We need to find the area of triangle MRC.

Solution

To find the area of triangle MRC, we can use the formula for the area of a triangle: Area = (base * height) / 2.

In this case, the base of the triangle is MK, and the height is RN. We are given the lengths of MN and NK, so we can find the length of MK by adding them together: MK = MN + NK.

Let's calculate the length of MK and then use it to find the area of triangle MRC.

Calculation

Given: - Angle M = 45 degrees - Length of MN = 12 cm - Length of NK = 18 cm

To find the length of MK, we add the lengths of MN and NK: MK = MN + NK = 12 cm + 18 cm = 30 cm.

Now, we can calculate the area of triangle MRC using the formula: Area = (base * height) / 2 = (MK * RN) / 2.

To find the length of RN, we can use trigonometry. Since angle M is 45 degrees, angle R is also 45 degrees (since the height RN is perpendicular to MK). Therefore, triangle MNR is an isosceles right triangle.

In an isosceles right triangle, the length of the hypotenuse (MN or NK) is equal to the length of one of the legs (RN). So, RN = MN = 12 cm.

Now, we can substitute the values into the formula to find the area: Area = (MK * RN) / 2 = (30 cm * 12 cm) / 2 = 360 cm².

Therefore, the area of triangle MRC is 360 cm².

Diagram

Here is a diagram illustrating the given triangle MRC:

         M
        / \
       /   \
      /     \
     /       \
    /         \
   /           \
  /             \
 /               \
N-----------------R
 \               /
  \             /
   \           /
    \         /
     \       /
      \     /
       \   /
        \ /
         C

Please note that the diagram is not to scale.

I hope this helps! Let me know if you have any further questions.