The length and breadth of a rectangle are in the ration 8:5. The length is 10.5 centimeters more than the breadth. What are the length and breads of the rectangle? Kindly give steps also.
(L+10.5)/L=8/5
solve for L first
8L=5L+52.5
3L=52.5
L=17.3 check that.
W=that + 10.5
To find the length and breadth of the rectangle, let's follow these steps:
Step 1: Understand the given information.
The given information states that the ratio of the length to the breadth is 8:5. It is also given that the length is 10.5 centimeters more than the breadth.
Step 2: Assign variables.
Let the breadth of the rectangle be x centimeters. Since the length is 10.5 centimeters more than the breadth, the length of the rectangle can be expressed as x + 10.5 centimeters.
Step 3: Write the ratio equation.
According to the given information, the ratio of length to breadth is 8:5. Therefore, we can write the equation as:
(length)/(breadth) = 8/5
Step 4: Substitute the values.
Substitute the values using the variables we assigned in step 2:
(x + 10.5)/x = 8/5
Step 5: Cross-multiply the equation.
Cross-multiplying the equation gives us:
5(x + 10.5) = 8x
Step 6: Distribute and simplify the equation.
Expand the equation:
5x + 52.5 = 8x
Step 7: Isolate the variable.
Rearrange the equation to isolate the variable on one side:
8x - 5x = 52.5
3x = 52.5
Step 8: Solve for x.
Divide both sides of the equation by 3:
x = 52.5/3
x = 17.5
Step 9: Find the length.
Substitute the value of x back into the expression for the length:
Length = x + 10.5
Length = 17.5 + 10.5
Length = 28 centimeters
Step 10: Check the solution.
To check the solution, we can calculate the ratio of the length to the breadth:
Length : Breadth = 28 : 17.5 = 8 : 5
Therefore, the length of the rectangle is 28 centimeters and the breadth of the rectangle is 17.5 centimeters.