A triangular garden ABC has area 175 m^2. A straight hedge DE is planted parallel to BC, with D on AB and E on AC, so that AD : AB = 2 : 5. Find the area of the region DBCE (in m^2).

Question

Accepted Answer

147. area(ADE) : area(ABC) = (2/5 )^2 = 4/25, so area(ADE) = 175 × 4/25 = 28 m^2. Region DBCE is whatever is left: 175 - 28 = 147 m^2. The option 28 is the small triangle, not the region asked for, while 70 and 105 come from splitting 175 in the ratio 2 : 5 without squaring.

A triangular garden ABC has area $175 m^{2}$ . A straight hedge DE is planted parallel to BC, with D on AB and E on AC, so that AD : AB = 2 : 5.
Find the area of the region DBCE (in $m^{2}$ ).

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More Class 10 Areas of Similar Triangles practice

A triangular garden ABC has area 175m2. A straight hedge DE is planted parallel to BC, with D on AB and E on AC, so that AD : AB = 2 : 5.Find the area of the region DBCE (in m2).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

A triangular garden ABC has area $175 m^{2}$ . A straight hedge DE is planted parallel to BC, with D on AB and E on AC, so that AD : AB = 2 : 5.
Find the area of the region DBCE (in $m^{2}$ ).