Question

sunita has a plot of land which she decides use for building an old age home and a dispensary for they needy. plot ABCD is a rhombus. if R is a point on the diagonal BD show that equal arears are alloted for building an old age home and despensary

Answer 1

Answer:

Step-by-step explanation:

Since, sunita has a plot of land which she decides use for building an old age home and a dispensary for they needy. plot ABCD is a rhombus, our aim is to find if R is a point on the diagonal BD show that equal areas are alloyed for building an old age home and dispensary.

Let x be equal to DR and y equal to RB.

Now, our aim is to verify if the diagonal divides the area in two equal parts.

Now, in triangle we know that if a line from the vertex divides the opposite side in x : y ratio the narea of two triangles formed are also divided in the same ratio. So here using this concept, in the triangle CBD. CR divides the line DB in the ratio x : y so.

Area of the triangle BRC is equal equal to $\frac{y}{x+y}$ times the area of the triangle BCD.

Now we can say that area of triangle BRC is equal to the ABR which is equal to the area for dispensary.