A rectangle is divided into 4 parts, A B, C and D. The areas of A: B: C are in the ratio 10:18:5. C is a square with an area of 25cm squared. What is the area of rectangle D?
Make a sketch,
let part A be x by y
let part B be x by 5
let part C be 5 by 5 , the square
then part D is 5 by y
xy : 5x : 25 = 10:18:5
so
xy/10 = 5x/18 = 25/5
using 5x/18 = 25/5
5x = 90
x = 18
then in xy/10 = 25/5
18y/10 = 5
y = 50/18 = 25/9
area of D = 5y = 5(25/9) = 125/9 or 13 8/9
To find the area of rectangle D, we first need to find the areas of rectangles A and B. Since the areas of A, B, and C are given in a ratio, we can let the areas be 10x, 18x, and 5x, respectively, where x is a common multiplier.
Given that C is a square with an area of 25 cm², we can solve for x by setting the area of C equal to 5x and solving for x:
5x = 25 cm²
Dividing both sides of the equation by 5, we find:
x = 25 cm² / 5 = 5 cm²
Now, we can find the areas of A and B:
Area of A = 10x = 10 * 5 cm² = 50 cm²
Area of B = 18x = 18 * 5 cm² = 90 cm²
The entire rectangle is made up of A, B, C, and D. The total area is the sum of the areas of all four parts:
Total area = Area of A + Area of B + Area of C + Area of D
Since the total area of the rectangle is not provided, we cannot directly calculate the area of D. More information is needed to solve the problem.